Defining parameters
Level: | \( N \) | = | \( 272 = 2^{4} \cdot 17 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 13 \) | ||
Sturm bound: | \(18432\) | ||
Trace bound: | \(6\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(272))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7136 | 3928 | 3208 |
Cusp forms | 6688 | 3794 | 2894 |
Eisenstein series | 448 | 134 | 314 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(272))\)
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 \(S_{4}^{\mathrm{old}}(\Gamma_1(272))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(272)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 1}\)