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Properties

Label 96.13.g
Level $96$
Weight $13$
Character orbit 96.g
Rep. character $\chi_{96}(31,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $208$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 96.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(208\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(96, [\chi])\).

Total New Old
Modular forms 200 24 176
Cusp forms 184 24 160
Eisenstein series 16 0 16

Trace form

\( 24 q - 20592 q^{5} - 4251528 q^{9} + O(q^{10}) \) \( 24 q - 20592 q^{5} - 4251528 q^{9} + 9290160 q^{13} + 14517360 q^{17} + 150115680 q^{21} + 181354056 q^{25} + 1176935760 q^{29} + 644202720 q^{33} + 6513627120 q^{37} - 25272428688 q^{41} + 3647811024 q^{45} - 57739879656 q^{49} + 40289996880 q^{53} + 38879961120 q^{57} + 227433483120 q^{61} - 87232951008 q^{65} + 158787541680 q^{73} - 737500740480 q^{77} + 753145430616 q^{81} - 1077983096928 q^{85} - 1224674367696 q^{89} - 738429527520 q^{93} + 3588655898160 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.13.g.a 96.g 4.b $12$ $87.743$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 96.13.g.a \(0\) \(0\) \(-37752\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-3146-\beta _{2})q^{5}+(63\beta _{1}+\cdots)q^{7}+\cdots\)
96.13.g.b 96.g 4.b $12$ $87.743$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 96.13.g.b \(0\) \(0\) \(17160\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{3}+(1430-\beta _{1})q^{5}+(18\beta _{6}+8\beta _{7}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{13}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{13}^{\mathrm{old}}(96, [\chi]) \simeq \) \(S_{13}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)