Properties

Label 624.2.bn
Level $624$
Weight $2$
Character orbit 624.bn
Rep. character $\chi_{624}(187,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $112$
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.bn (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
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 232 112 120
Cusp forms 216 112 104
Eisenstein series 16 0 16

Trace form

\( 112 q + O(q^{10}) \) \( 112 q - 8 q^{10} + 32 q^{14} + 4 q^{20} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 16 q^{26} - 8 q^{28} + 60 q^{32} - 24 q^{34} - 40 q^{38} + 40 q^{40} - 16 q^{43} - 4 q^{44} - 56 q^{46} - 56 q^{50} + 56 q^{52} + 32 q^{55} + 40 q^{56} + 40 q^{58} - 64 q^{59} + 44 q^{60} - 72 q^{64} + 24 q^{68} - 64 q^{70} - 64 q^{71} - 16 q^{73} - 16 q^{75} - 16 q^{76} + 24 q^{78} + 4 q^{80} - 112 q^{81} - 72 q^{82} + 80 q^{83} + 16 q^{86} - 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} + 40 q^{98} + O(q^{100}) \)

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.bn.a 624.bn 208.s $112$ $4.983$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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