Defining parameters
Level: | \( N \) | = | \( 1312 = 2^{5} \cdot 41 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 32 \) | ||
Sturm bound: | \(215040\) | ||
Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1312))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 55040 | 30594 | 24446 |
Cusp forms | 52481 | 29814 | 22667 |
Eisenstein series | 2559 | 780 | 1779 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1312))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(1312))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(1312)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(656))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1312))\)\(^{\oplus 1}\)