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Properties

Label 624.2.ce
Level $624$
Weight $2$
Character orbit 624.ce
Rep. character $\chi_{624}(149,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $432$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.ce (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 464 464 0
Cusp forms 432 432 0
Eisenstein series 32 32 0

Trace form

\( 432 q - 2 q^{3} - 12 q^{4} - 6 q^{6} + O(q^{10}) \) \( 432 q - 2 q^{3} - 12 q^{4} - 6 q^{6} - 12 q^{10} - 8 q^{13} - 8 q^{15} - 4 q^{16} - 12 q^{18} - 12 q^{19} + 4 q^{22} - 24 q^{24} - 368 q^{25} - 8 q^{27} + 20 q^{28} + 4 q^{30} - 16 q^{31} - 8 q^{33} - 12 q^{34} + 16 q^{36} - 12 q^{37} - 56 q^{40} - 34 q^{42} + 4 q^{43} + 24 q^{45} - 12 q^{46} + 18 q^{48} - 24 q^{49} + 12 q^{52} + 28 q^{54} + 120 q^{55} - 12 q^{57} - 28 q^{58} + 28 q^{60} - 4 q^{61} - 36 q^{63} - 48 q^{64} + 32 q^{66} - 12 q^{67} - 6 q^{69} + 10 q^{72} - 14 q^{75} - 60 q^{76} - 4 q^{78} - 32 q^{79} - 4 q^{81} + 56 q^{82} + 40 q^{84} + 48 q^{85} - 44 q^{88} + 48 q^{90} + 44 q^{91} + 12 q^{93} - 16 q^{94} - 68 q^{96} - 16 q^{97} + 156 q^{99} + O(q^{100}) \)

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.ce.a 624.ce 624.be $432$ $4.983$ None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$