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Properties

Label 624.2.x
Level $624$
Weight $2$
Character orbit 624.x
Rep. character $\chi_{624}(157,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $2$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 232 96 136
Cusp forms 216 96 120
Eisenstein series 16 0 16

Trace form

\( 96 q + 8 q^{4} + 24 q^{8} + O(q^{10}) \) \( 96 q + 8 q^{4} + 24 q^{8} + 16 q^{10} + 16 q^{11} - 8 q^{12} + 8 q^{14} + 16 q^{15} - 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{24} + 32 q^{29} + 8 q^{30} - 48 q^{31} + 40 q^{34} - 48 q^{35} + 8 q^{36} + 32 q^{37} + 56 q^{38} - 32 q^{40} + 48 q^{44} + 8 q^{46} + 32 q^{48} - 96 q^{49} + 32 q^{50} - 16 q^{51} + 8 q^{52} - 32 q^{53} - 8 q^{54} + 32 q^{58} - 32 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 48 q^{66} + 32 q^{67} - 80 q^{68} - 32 q^{69} + 24 q^{70} + 8 q^{72} - 144 q^{74} - 16 q^{75} + 16 q^{76} - 32 q^{77} - 32 q^{79} - 16 q^{80} - 96 q^{81} - 80 q^{82} + 48 q^{84} + 32 q^{85} + 64 q^{86} - 72 q^{88} + 8 q^{90} + 80 q^{92} - 56 q^{94} + 96 q^{95} + 8 q^{98} + 16 q^{99} + O(q^{100}) \)

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.x.a 624.x 16.e $40$ $4.983$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
624.2.x.b 624.x 16.e $56$ $4.983$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)