my mom who has a swan as her vehicle
The Goddess Saraswati is often depicted as a beautiful, white-skinned woman dressed in pure white. She is often seated on a white lotus (although Her mythical representation is believed to be a swan), which symbolizes that she is founded in the experience of the Absolute Truth. Thus, she not only has the knowledge but also the experience of the Highest Reality.
She is mainly associated with the color white, which signifies the purity of true knowledge. Occasionally, however, she is also associated with the colour yellow, the colour of the flowers of the mustard plant that bloom at the time of her festival in the spring.
She is not adorned heavily with jewels and gold but is dressed modestly — perhaps representing her preference of knowledge over worldly material things.
She is generally shown to have four arms, which represent the four aspects of human personality in learning: mind, intellect, alertness, and ego.
She is shown to hold the following in her hands:
A book, which is the sacred Vedas, representing the universal, divine, eternal, and true knowledge as well as her perfection of the sciences and the scriptures.
A mala (rosary) of crystals, representing the power of meditation and spirituality.
A pot of sacred water, representing creative and purificatory powers.
The vina, a musical instrument that represents her perfection of all arts and sciences. Saraswati is also associated with the love for the rhythm of music, representing all emotions and feelings expressed in speech or music.
A 'white swan' (Sanskrit: hamsa) is often located next to her feet. The swan symbolizes discrimination between the good and the bad or the eternal and the evanescent. Due to her association with the swan, Goddess Saraswati is also referred to as Hamsa-vahini, which means "she who has a swan as her vehicle".
She is usually depicted near a flowing river, which may be related to her early history as a river goddess. The river associates her with flow, and describes her love of flow in all experiences.
Sometimes a peacock is shown beside the goddess. The peacock represents arrogance and pride over its beauty, and by having a peacock as one of her animal representations, the Goddess teaches Hindus not to be concerned with external appearance and to be wise regarding the eternal truth.