Defining parameters
Level: | \( N \) | = | \( 3136 = 2^{6} \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 14 \) | ||
Newform subspaces: | \( 19 \) | ||
Sturm bound: | \(602112\) | ||
Trace bound: | \(57\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3136))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4728 | 1182 | 3546 |
Cusp forms | 408 | 115 | 293 |
Eisenstein series | 4320 | 1067 | 3253 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 107 | 8 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3136))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(3136))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(3136)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1568))\)\(^{\oplus 2}\)