Properties

Label 96.3.m
Level $96$
Weight $3$
Character orbit 96.m
Rep. character $\chi_{96}(19,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $64$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 96.m (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(96, [\chi])\).

Total New Old
Modular forms 136 64 72
Cusp forms 120 64 56
Eisenstein series 16 0 16

Trace form

\( 64q + O(q^{10}) \) \( 64q + 40q^{10} + 48q^{12} + 32q^{14} - 8q^{16} - 24q^{18} - 160q^{20} - 184q^{22} + 128q^{23} - 72q^{24} - 200q^{26} - 120q^{28} + 40q^{32} + 120q^{34} - 192q^{35} + 280q^{38} + 584q^{40} - 192q^{43} + 104q^{44} + 32q^{46} - 312q^{50} - 192q^{51} - 424q^{52} + 320q^{53} - 72q^{54} - 256q^{55} - 392q^{56} - 352q^{58} - 256q^{59} - 144q^{60} + 64q^{61} - 48q^{62} + 408q^{64} + 144q^{66} + 64q^{67} + 856q^{68} - 192q^{69} + 984q^{70} + 512q^{71} + 1056q^{74} + 384q^{75} + 296q^{76} - 448q^{77} + 360q^{78} + 512q^{79} + 328q^{80} - 760q^{82} - 448q^{86} - 1072q^{88} + 192q^{91} - 784q^{92} - 480q^{94} + 600q^{96} + 272q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
96.3.m.a \(64\) \(2.616\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)