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Properties

Label 96.3.p
Level $96$
Weight $3$
Character orbit 96.p
Rep. character $\chi_{96}(5,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $120$
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.p (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
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 136 136 0
Cusp forms 120 120 0
Eisenstein series 16 16 0

Trace form

\( 120q - 4q^{3} - 8q^{4} - 4q^{6} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 120q - 4q^{3} - 8q^{4} - 4q^{6} - 8q^{7} - 4q^{9} + 32q^{10} - 4q^{12} - 8q^{13} - 40q^{16} - 4q^{18} - 8q^{19} - 4q^{21} - 120q^{22} - 144q^{24} - 8q^{25} + 92q^{27} - 8q^{28} - 60q^{30} - 16q^{31} - 8q^{33} - 40q^{34} + 64q^{36} - 8q^{37} - 196q^{39} - 232q^{40} + 16q^{42} - 8q^{43} - 4q^{45} - 40q^{46} + 48q^{48} - 40q^{51} - 112q^{52} + 304q^{54} - 264q^{55} - 4q^{57} - 16q^{58} + 424q^{60} + 56q^{61} - 8q^{63} + 40q^{64} + 428q^{66} + 248q^{67} - 4q^{69} + 328q^{70} + 416q^{72} - 8q^{73} - 104q^{75} + 720q^{76} + 276q^{78} + 512q^{82} + 232q^{84} - 208q^{85} - 452q^{87} + 272q^{88} - 304q^{90} - 200q^{91} - 40q^{93} + 416q^{94} - 616q^{96} - 16q^{97} + 252q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.p.a \(120\) \(2.616\) None \(0\) \(-4\) \(0\) \(-8\)