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Properties

Label 96.4.d
Level $96$
Weight $4$
Character orbit 96.d
Rep. character $\chi_{96}(49,\cdot)$
Character field $\Q$
Dimension $6$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
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 6 50
Cusp forms 40 6 34
Eisenstein series 16 0 16

Trace form

\( 6 q - 28 q^{7} - 54 q^{9} + O(q^{10}) \) \( 6 q - 28 q^{7} - 54 q^{9} + 60 q^{15} + 52 q^{17} - 328 q^{23} - 106 q^{25} + 636 q^{31} - 312 q^{39} + 236 q^{41} + 408 q^{47} + 654 q^{49} - 1024 q^{55} - 168 q^{57} + 252 q^{63} - 1744 q^{65} + 1704 q^{71} + 956 q^{73} + 44 q^{79} + 486 q^{81} - 1044 q^{87} - 220 q^{89} - 5104 q^{95} - 2444 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.d.a 96.d 8.b $6$ $5.664$ 6.0.8248384.1 None 24.4.d.a \(0\) \(0\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(-5+\beta _{1}+\cdots)q^{7}+\cdots\)

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

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