Defining parameters
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(22\) | ||
Distinguishing \(T_p\): | \(2\), \(37\), \(47\), \(67\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 264 | 52 | 212 |
Cusp forms | 216 | 52 | 164 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)