Defining parameters
Level: | \( N \) | = | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 24 \) | ||
Sturm bound: | \(368640\) | ||
Trace bound: | \(49\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1216))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 139536 | 77702 | 61834 |
Cusp forms | 136944 | 76954 | 59990 |
Eisenstein series | 2592 | 748 | 1844 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1216))\)
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 \(S_{4}^{\mathrm{old}}(\Gamma_1(1216))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(1216)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 2}\)