Properties

Label 624.2.c
Level $624$
Weight $2$
Character orbit 624.c
Rep. character $\chi_{624}(337,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $7$
Sturm bound $224$
Trace bound $17$

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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

\( 14 q - 2 q^{3} + 14 q^{9} + O(q^{10}) \) \( 14 q - 2 q^{3} + 14 q^{9} + 2 q^{13} - 4 q^{17} - 10 q^{25} - 2 q^{27} + 4 q^{29} + 2 q^{39} + 24 q^{43} + 10 q^{49} + 12 q^{51} - 12 q^{53} + 32 q^{55} - 12 q^{61} - 16 q^{65} + 22 q^{75} + 8 q^{77} + 16 q^{79} + 14 q^{81} - 12 q^{87} - 40 q^{91} - 64 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
624.2.c.a 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}+iq^{7}+q^{9}+(-3-i)q^{13}+\cdots\)
624.2.c.b 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots\)
624.2.c.c 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
624.2.c.d 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}-2iq^{7}+q^{9}+3iq^{11}+\cdots\)
624.2.c.e 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots\)
624.2.c.f 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots\)
624.2.c.g 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{7}+q^{9}+iq^{11}+(3-i)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)