Defining parameters
Level: | \( N \) | = | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(1176\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(98))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 354 | 95 | 259 |
Cusp forms | 235 | 95 | 140 |
Eisenstein series | 119 | 0 | 119 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(98)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)