Defining parameters
Level: | \( N \) | = | \( 351 = 3^{3} \cdot 13 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(9072\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(351))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 379 | 188 | 191 |
Cusp forms | 19 | 12 | 7 |
Eisenstein series | 360 | 176 | 184 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(351))\)
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 the newforms together with their dimension.
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(351))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(351)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)