Defining parameters
Level: | \( N \) | = | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 28 \) | ||
Sturm bound: | \(9216\) | ||
Trace bound: | \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(288))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2560 | 1071 | 1489 |
Cusp forms | 2049 | 981 | 1068 |
Eisenstein series | 511 | 90 | 421 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)
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.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(288)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)