Defining parameters
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.n (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 156 \) |
Character field: | \(\Q\) | ||
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 | 348 | 84 | 264 |
Cusp forms | 324 | 84 | 240 |
Eisenstein series | 24 | 0 | 24 |
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.n.a | $2$ | $36.817$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(-40\) | \(q-\zeta_{6}q^{3}-20q^{7}-3^{3}q^{9}+(-35-6\zeta_{6})q^{13}+\cdots\) |
624.4.n.b | $2$ | $36.817$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(40\) | \(q+\zeta_{6}q^{3}+20q^{7}-3^{3}q^{9}+(-35-6\zeta_{6})q^{13}+\cdots\) |
624.4.n.c | $24$ | $36.817$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
624.4.n.d | $56$ | $36.817$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(624, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(624, [\chi]) \cong \)