Properties

Label 96.4.n
Level $96$
Weight $4$
Character orbit 96.n
Rep. character $\chi_{96}(13,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $96$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 96.n (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(96, [\chi])\).

Total New Old
Modular forms 200 96 104
Cusp forms 184 96 88
Eisenstein series 16 0 16

Trace form

\( 96q + O(q^{10}) \) \( 96q - 120q^{10} + 48q^{12} + 416q^{14} + 120q^{16} + 72q^{18} - 160q^{20} + 40q^{22} - 656q^{23} - 456q^{24} - 40q^{26} - 760q^{28} + 1488q^{31} - 1240q^{32} - 1000q^{34} + 912q^{35} + 440q^{38} + 1352q^{40} - 1616q^{43} + 1000q^{44} + 1440q^{46} + 2856q^{50} + 1488q^{51} + 2520q^{52} - 1504q^{53} + 216q^{54} + 288q^{55} - 392q^{56} - 2016q^{58} - 2752q^{59} - 2448q^{60} + 1824q^{61} - 2928q^{62} - 1008q^{63} - 6888q^{64} - 2736q^{66} - 816q^{67} - 5032q^{68} + 1056q^{69} - 1800q^{70} - 448q^{71} + 6944q^{74} + 2208q^{75} + 5032q^{76} - 3808q^{77} + 3528q^{78} + 11336q^{80} + 9320q^{82} + 2368q^{86} - 944q^{88} + 3600q^{91} - 7696q^{92} - 16480q^{94} - 5160q^{96} - 10288q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
96.4.n.a \(96\) \(5.664\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)