Properties

Label 624.2.bh
Level $624$
Weight $2$
Character orbit 624.bh
Rep. character $\chi_{624}(131,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
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.bh (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
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 232 192 40
Cusp forms 216 192 24
Eisenstein series 16 0 16

Trace form

\( 192 q + O(q^{10}) \) \( 192 q - 8 q^{10} - 40 q^{16} - 20 q^{18} + 16 q^{19} - 8 q^{22} - 20 q^{24} - 68 q^{30} + 24 q^{34} - 40 q^{36} + 32 q^{40} - 16 q^{43} + 56 q^{46} + 20 q^{48} + 192 q^{49} - 40 q^{51} + 8 q^{52} + 100 q^{54} - 32 q^{55} + 44 q^{60} - 32 q^{61} - 48 q^{64} - 40 q^{66} - 64 q^{67} - 96 q^{70} - 60 q^{72} + 56 q^{75} - 152 q^{76} + 12 q^{84} - 32 q^{85} + 112 q^{87} + 24 q^{88} - 60 q^{90} + 96 q^{94} + 68 q^{96} + O(q^{100}) \)

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.bh.a 624.bh 48.k $192$ $4.983$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)