Properties

Label 91.2.q
Level $91$
Weight $2$
Character orbit 91.q
Rep. character $\chi_{91}(36,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(91, [\chi])\).

Total New Old
Modular forms 24 12 12
Cusp forms 16 12 4
Eisenstein series 8 0 8

Trace form

\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27}+ \cdots + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.2.q.a 91.q 13.e $12$ $0.727$ 12.0.\(\cdots\).1 None 91.2.q.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{4}-\beta _{6}+\beta _{10})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(91, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(91, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)