Defining parameters
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 268 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(272\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(804, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 140 | 68 | 72 |
Cusp forms | 132 | 68 | 64 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(804, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
804.2.e.a | $34$ | $6.420$ | None | \(0\) | \(-34\) | \(0\) | \(-4\) | ||
804.2.e.b | $34$ | $6.420$ | None | \(0\) | \(34\) | \(0\) | \(4\) |
Decomposition of \(S_{2}^{\mathrm{old}}(804, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(804, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(268, [\chi])\)\(^{\oplus 2}\)