Linear relations between L-values of newforms and moments of elliptic K integral

Key Points

• The dimension formula derived offers a new perspective on the relationship between newforms and elliptic integrals.
• By evaluating moments of elliptic integrals, we uncover critical l-values linked to cuspidal newforms.
• This analysis employs modular forms on different groups, showcasing the rich structure of these l-values.
• The findings may inspire further investigations into modular forms and their applications in number theory.