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Properties

Label 624.2.cx
Level $624$
Weight $2$
Character orbit 624.cx
Rep. character $\chi_{624}(179,\cdot)$
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.cx (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

\( 432 q - 2 q^{3} - 4 q^{4} + 12 q^{6} - 24 q^{7} + O(q^{10}) \) \( 432 q - 2 q^{3} - 4 q^{4} + 12 q^{6} - 24 q^{7} - 4 q^{10} - 20 q^{12} - 8 q^{13} - 4 q^{16} - 12 q^{19} - 24 q^{22} + 42 q^{24} + 16 q^{27} - 48 q^{28} - 10 q^{30} - 12 q^{33} - 24 q^{36} - 12 q^{37} - 56 q^{39} + 24 q^{40} - 6 q^{42} + 12 q^{43} + 24 q^{45} - 12 q^{46} + 44 q^{48} + 160 q^{49} - 20 q^{51} + 36 q^{52} - 6 q^{54} - 40 q^{55} - 12 q^{58} - 4 q^{61} - 88 q^{64} - 104 q^{66} - 12 q^{67} - 14 q^{69} + 42 q^{72} + 14 q^{75} + 36 q^{76} + 108 q^{78} - 4 q^{81} - 36 q^{82} - 48 q^{84} - 72 q^{85} - 4 q^{87} - 40 q^{88} - 220 q^{90} - 12 q^{91} - 24 q^{93} + 16 q^{94} - 24 q^{97} + O(q^{100}) \)

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.cx.a 624.cx 624.bx $432$ $4.983$ None \(0\) \(-2\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{12}]$