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Properties

Label 624.2.bv
Level $624$
Weight $2$
Character orbit 624.bv
Rep. character $\chi_{624}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $7$
Sturm bound $224$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.bv (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(224\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(624, [\chi])\).

Total New Old
Modular forms 248 28 220
Cusp forms 200 28 172
Eisenstein series 48 0 48

Trace form

\( 28 q + 2 q^{3} - 6 q^{7} - 14 q^{9} + O(q^{10}) \) \( 28 q + 2 q^{3} - 6 q^{7} - 14 q^{9} - 2 q^{13} - 2 q^{17} - 32 q^{25} - 4 q^{27} + 2 q^{29} + 6 q^{37} + 4 q^{39} + 6 q^{41} - 18 q^{43} - 6 q^{45} + 26 q^{49} + 24 q^{51} - 12 q^{53} + 4 q^{55} + 84 q^{59} + 6 q^{61} + 6 q^{63} + 22 q^{65} - 30 q^{67} - 22 q^{75} + 16 q^{77} + 44 q^{79} - 14 q^{81} - 6 q^{85} - 24 q^{87} - 50 q^{91} + 4 q^{95} - 36 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bv.a 624.bv 13.e $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(-4+\cdots)q^{7}+\cdots\)
624.2.bv.b 624.bv 13.e $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(-2+4\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
624.2.bv.c 624.bv 13.e $4$ $4.983$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}^{2}q^{3}+(-1+2\zeta_{12}^{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
624.2.bv.d 624.bv 13.e $4$ $4.983$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{12}^{2})q^{3}+(1-2\zeta_{12}^{2})q^{5}+\cdots\)
624.2.bv.e 624.bv 13.e $4$ $4.983$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{2}q^{3}+(1-2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\)
624.2.bv.f 624.bv 13.e $4$ $4.983$ \(\Q(\sqrt{-3}, \sqrt{-43})\) None \(0\) \(2\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{2})q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
624.2.bv.g 624.bv 13.e $8$ $4.983$ 8.0.649638144.4 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{2})q^{3}+(\beta _{2}-\beta _{5})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)