Properties

Label 96.4.c
Level $96$
Weight $4$
Character orbit 96.c
Rep. character $\chi_{96}(95,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 96.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(96, [\chi])\).

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

Trace form

\( 12 q - 20 q^{9} + 72 q^{13} + 136 q^{21} - 132 q^{25} + 80 q^{33} - 24 q^{37} - 544 q^{45} - 540 q^{49} - 888 q^{57} + 456 q^{61} + 1312 q^{69} + 2424 q^{73} + 2924 q^{81} - 3072 q^{85} - 2360 q^{93} - 2952 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.4.c.a 96.c 12.b $12$ $5.664$ 12.0.\(\cdots\).1 None 96.4.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}-\beta _{8}q^{5}-\beta _{1}q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

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