Properties

Label 91.2.c
Level $91$
Weight $2$
Character orbit 91.c
Rep. character $\chi_{91}(64,\cdot)$
Character field $\Q$
Dimension $6$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
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 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

\( 6q - 4q^{4} - 2q^{9} + O(q^{10}) \) \( 6q - 4q^{4} - 2q^{9} - 20q^{12} + 8q^{13} - 4q^{14} + 8q^{16} - 8q^{17} + 24q^{22} + 6q^{23} + 8q^{25} + 12q^{26} - 12q^{27} - 14q^{29} + 16q^{30} - 6q^{35} + 4q^{36} - 4q^{38} - 8q^{39} - 20q^{40} - 4q^{42} - 26q^{43} + 8q^{48} - 6q^{49} + 8q^{51} - 20q^{52} + 2q^{53} + 12q^{55} + 12q^{56} + 28q^{61} + 16q^{62} - 8q^{64} - 6q^{65} + 28q^{66} + 20q^{68} - 4q^{69} - 24q^{74} + 44q^{75} + 16q^{77} + 16q^{78} + 26q^{79} - 26q^{81} - 56q^{82} - 40q^{87} - 40q^{88} - 12q^{90} - 2q^{91} - 36q^{92} + 20q^{94} + 58q^{95} + O(q^{100}) \)

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.c.a \(6\) \(0.727\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)