Defining parameters
Level: | \( N \) | = | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 9 \) | ||
Newform subspaces: | \( 18 \) | ||
Sturm bound: | \(56448\) | ||
Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(980))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1314 | 386 | 928 |
Cusp forms | 114 | 96 | 18 |
Eisenstein series | 1200 | 290 | 910 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 84 | 0 | 12 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(980))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(980))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(980)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)