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Properties

Label 624.2.ch
Level $624$
Weight $2$
Character orbit 624.ch
Rep. character $\chi_{624}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $224$
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.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
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 464 224 240
Cusp forms 432 224 208
Eisenstein series 32 0 32

Trace form

\( 224 q + O(q^{10}) \) \( 224 q - 8 q^{10} - 32 q^{14} - 48 q^{16} - 12 q^{20} + 8 q^{22} + 12 q^{24} - 224 q^{25} - 16 q^{26} - 52 q^{28} + 40 q^{32} + 64 q^{34} - 40 q^{38} - 40 q^{40} - 16 q^{43} + 24 q^{44} + 16 q^{46} - 16 q^{50} - 16 q^{52} - 32 q^{55} - 20 q^{56} - 32 q^{58} + 96 q^{59} - 64 q^{60} - 24 q^{68} - 48 q^{70} + 64 q^{71} - 16 q^{73} + 96 q^{74} - 16 q^{75} + 76 q^{76} - 24 q^{78} + 100 q^{80} + 112 q^{81} + 48 q^{82} - 64 q^{86} - 60 q^{88} - 16 q^{89} + 40 q^{91} - 48 q^{92} + 64 q^{94} - 56 q^{98} + O(q^{100}) \)

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.ch.a 624.ch 208.af $224$ $4.983$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)