Properties

Label 96.2.n
Level 96
Weight 2
Character orbit n
Rep. character \(\chi_{96}(13,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 32
Newform subspaces 1
Sturm bound 32
Trace bound 0

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Defining parameters

Level: \( N \) = \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) = \( 2 \)
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: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(96, [\chi])\).

Total New Old
Modular forms 72 32 40
Cusp forms 56 32 24
Eisenstein series 16 0 16

Trace form

\( 32q + O(q^{10}) \) \( 32q - 8q^{10} - 16q^{12} - 32q^{14} - 8q^{16} - 8q^{18} - 32q^{20} - 8q^{22} - 16q^{23} - 8q^{24} + 40q^{26} + 40q^{28} - 48q^{31} + 40q^{32} + 40q^{34} - 48q^{35} + 40q^{38} + 8q^{40} - 16q^{43} + 8q^{44} - 32q^{46} + 24q^{50} + 16q^{51} - 8q^{52} - 32q^{53} + 8q^{54} + 32q^{55} + 56q^{56} - 32q^{58} + 64q^{59} + 48q^{60} - 32q^{61} + 48q^{62} + 16q^{63} + 24q^{64} + 48q^{66} + 16q^{67} - 8q^{68} - 32q^{69} - 24q^{70} + 64q^{71} - 32q^{74} + 32q^{75} - 56q^{76} - 32q^{77} + 24q^{78} - 56q^{80} - 40q^{82} - 64q^{86} - 48q^{88} - 48q^{91} - 80q^{92} - 32q^{94} - 40q^{96} - 80q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
96.2.n.a \(32\) \(0.767\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database