Defining parameters
Level: | \( N \) | = | \( 164 = 2^{2} \cdot 41 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(3360\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(164))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 940 | 530 | 410 |
Cusp forms | 741 | 450 | 291 |
Eisenstein series | 199 | 80 | 119 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)
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 available newforms together with their dimension.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(164))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(164)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 2}\)