Properties

Label 91.2.i
Level $91$
Weight $2$
Character orbit 91.i
Rep. character $\chi_{91}(34,\cdot)$
Character field $\Q(\zeta_{4})$
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.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
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 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\( 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} + O(q^{10}) \) \( 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 16 q^{16} - 8 q^{18} - 16 q^{22} - 20 q^{28} - 4 q^{29} - 16 q^{32} - 4 q^{35} + 12 q^{37} + 40 q^{39} + 40 q^{42} + 12 q^{44} + 24 q^{46} - 28 q^{50} - 12 q^{53} - 8 q^{57} - 44 q^{58} + 44 q^{60} + 20 q^{63} - 40 q^{65} + 60 q^{67} + 4 q^{70} - 28 q^{72} - 48 q^{74} + 44 q^{78} - 4 q^{79} - 92 q^{81} - 4 q^{84} + 12 q^{85} + 36 q^{86} - 32 q^{91} + 24 q^{92} - 28 q^{93} - 28 q^{98} + 12 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
91.2.i.a \(12\) \(0.727\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-4\) \(0\) \(0\) \(-8\) \(q-\beta _{8}q^{2}+\beta _{10}q^{3}+(-\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)