Defining parameters
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(624, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 124 | 14 | 110 |
Cusp forms | 100 | 14 | 86 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(624, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
624.2.c.a | $2$ | $4.983$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-q^{3}+iq^{5}+iq^{7}+q^{9}+(-3-i)q^{13}+\cdots\) |
624.2.c.b | $2$ | $4.983$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-q^{3}+iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots\) |
624.2.c.c | $2$ | $4.983$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-q^{3}+2iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\) |
624.2.c.d | $2$ | $4.983$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-q^{3}+iq^{5}-2iq^{7}+q^{9}+3iq^{11}+\cdots\) |
624.2.c.e | $2$ | $4.983$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+q^{3}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots\) |
624.2.c.f | $2$ | $4.983$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+q^{3}+\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots\) |
624.2.c.g | $2$ | $4.983$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+q^{3}+iq^{7}+q^{9}+iq^{11}+(3-i)q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(624, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)