Defining parameters
| Level: | \( N \) | = | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Newform subspaces: | \( 15 \) | ||
| Sturm bound: | \(301056\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2352))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3822 | 507 | 3315 |
| Cusp forms | 462 | 70 | 392 |
| Eisenstein series | 3360 | 437 | 2923 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 70 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2352))\)
We only show spaces with odd 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.
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2352))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2352)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 2}\)