Defining parameters
Level: | \( N \) | = | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 32 \) | ||
Sturm bound: | \(368640\) | ||
Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1232))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 139920 | 73684 | 66236 |
Cusp forms | 136560 | 72872 | 63688 |
Eisenstein series | 3360 | 812 | 2548 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1232))\)
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 available newforms together with their dimension.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1232))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(1232)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1232))\)\(^{\oplus 1}\)