Defining parameters
| Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 624.bc (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 52 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(448\) | ||
| Trace bound: | \(7\) | ||
| Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(624, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 696 | 84 | 612 |
| Cusp forms | 648 | 84 | 564 |
| Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(624, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 624.4.bc.a | $14$ | $36.817$ | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) | None | \(0\) | \(0\) | \(2\) | \(-12\) | \(q-3\beta _{5}q^{3}+\beta _{2}q^{5}+(-1+\beta _{5}-\beta _{8}+\cdots)q^{7}+\cdots\) |
| 624.4.bc.b | $14$ | $36.817$ | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) | None | \(0\) | \(0\) | \(2\) | \(12\) | \(q+3\beta _{5}q^{3}+\beta _{2}q^{5}+(1-\beta _{5}+\beta _{8})q^{7}+\cdots\) |
| 624.4.bc.c | $28$ | $36.817$ | None | \(0\) | \(0\) | \(4\) | \(-8\) | ||
| 624.4.bc.d | $28$ | $36.817$ | None | \(0\) | \(0\) | \(4\) | \(8\) | ||
Decomposition of \(S_{4}^{\mathrm{old}}(624, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(624, [\chi]) \cong \)