Defining parameters
Level: | \( N \) | \(=\) | \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 828.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 92 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(828, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 152 | 62 | 90 |
Cusp forms | 136 | 58 | 78 |
Eisenstein series | 16 | 4 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(828, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
828.2.e.a | $4$ | $6.612$ | \(\Q(i, \sqrt{14})\) | None | \(4\) | \(0\) | \(0\) | \(0\) | \(q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}+\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots\) |
828.2.e.b | $6$ | $6.612$ | 6.0.8869743.1 | \(\Q(\sqrt{-23}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{5}q^{2}+\beta _{3}q^{4}+(2-\beta _{2})q^{8}+(\beta _{1}+\cdots)q^{13}+\cdots\) |
828.2.e.c | $8$ | $6.612$ | 8.0.\(\cdots\).2 | \(\Q(\sqrt{-69}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{2}-2q^{4}-\beta _{4}q^{5}-\beta _{5}q^{7}-2\beta _{2}q^{8}+\cdots\) |
828.2.e.d | $8$ | $6.612$ | 8.0.3317760000.6 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{4}q^{4}+\beta _{6}q^{7}+(-\beta _{1}-2\beta _{7})q^{8}+\cdots\) |
828.2.e.e | $8$ | $6.612$ | 8.0.157351936.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{2}+\beta _{3})q^{2}+(2-\beta _{1})q^{4}-2\beta _{6}q^{5}+\cdots\) |
828.2.e.f | $24$ | $6.612$ | None | \(-4\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(828, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(828, [\chi]) \cong \)