Properties

Label 96.3.g
Level $96$
Weight $3$
Character orbit 96.g
Rep. character $\chi_{96}(31,\cdot)$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
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

\( 4q - 8q^{5} - 12q^{9} + O(q^{10}) \) \( 4q - 8q^{5} - 12q^{9} + 40q^{13} - 24q^{17} - 48q^{21} + 108q^{25} - 40q^{29} - 48q^{33} + 72q^{37} - 88q^{41} + 24q^{45} - 60q^{49} + 24q^{53} + 48q^{57} - 56q^{61} + 304q^{65} - 120q^{73} - 64q^{77} + 36q^{81} - 336q^{85} - 312q^{89} + 240q^{93} - 248q^{97} + O(q^{100}) \)

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.g.a \(4\) \(2.616\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-8\) \(0\) \(q+\zeta_{12}^{2}q^{3}+(-2-\zeta_{12}^{3})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)