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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.3.m.a 96.m 32.h $64$ $2.616$ None 96.3.m.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

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

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