Defining parameters
Level: | \( N \) | = | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 16 \) | ||
Newform subspaces: | \( 39 \) | ||
Sturm bound: | \(71808\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(804))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18612 | 7978 | 10634 |
Cusp forms | 17293 | 7722 | 9571 |
Eisenstein series | 1319 | 256 | 1063 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(804))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(804))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(804)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(402))\)\(^{\oplus 2}\)