Defining parameters
Level: | \( N \) | = | \( 5780 = 2^{2} \cdot 5 \cdot 17^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 36 \) | ||
Sturm bound: | \(3995136\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5780))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1006784 | 532595 | 474189 |
Cusp forms | 990785 | 528171 | 462614 |
Eisenstein series | 15999 | 4424 | 11575 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5780))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5780))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(5780)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1445))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2890))\)\(^{\oplus 2}\)