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

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

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.e.a 96.e 3.b $4$ $2.616$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 96.3.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(2\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots\)
96.3.e.b 96.e 3.b $4$ $2.616$ \(\Q(\sqrt{-2}, \sqrt{7})\) None 96.3.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{5}+(-\beta _{1}-2\beta _{3})q^{7}+\cdots\)

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

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