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Properties

Label 96.3.b
Level $96$
Weight $3$
Character orbit 96.b
Rep. character $\chi_{96}(79,\cdot)$
Character field $\Q$
Dimension $4$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
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 40 4 36
Cusp forms 24 4 20
Eisenstein series 16 0 16

Trace form

\( 4 q + 12 q^{9} + O(q^{10}) \) \( 4 q + 12 q^{9} + 32 q^{11} - 8 q^{17} - 32 q^{19} - 44 q^{25} - 96 q^{35} + 40 q^{41} - 32 q^{43} - 44 q^{49} + 96 q^{51} - 48 q^{57} + 128 q^{59} + 96 q^{65} + 256 q^{67} + 200 q^{73} - 192 q^{75} + 36 q^{81} - 160 q^{83} - 200 q^{89} - 288 q^{91} + 56 q^{97} + 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.3.b.a 96.b 8.d $4$ $2.616$ 4.0.4752.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)