Properties

Label 96.3.e
Level $96$
Weight $3$
Character orbit 96.e
Rep. character $\chi_{96}(65,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $48$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 96.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(96, [\chi])\).

Total New Old
Modular forms 40 8 32
Cusp forms 24 8 16
Eisenstein series 16 0 16

Trace form

\( 8q + 8q^{9} + O(q^{10}) \) \( 8q + 8q^{9} + 16q^{13} + 16q^{21} - 56q^{25} - 64q^{33} - 112q^{37} - 128q^{45} + 152q^{49} + 208q^{57} + 272q^{61} + 384q^{69} - 240q^{73} - 376q^{81} - 256q^{85} - 496q^{93} + 400q^{97} + O(q^{100}) \)

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.e.a \(4\) \(2.616\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(2\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots\)
96.3.e.b \(4\) \(2.616\) \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{5}+(-\beta _{1}-2\beta _{3})q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)