Properties

Label 91.2.u
Level $91$
Weight $2$
Character orbit 91.u
Rep. character $\chi_{91}(30,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $14$
Newform subspaces $2$
Sturm bound $18$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 22 22 0
Cusp forms 14 14 0
Eisenstein series 8 8 0

Trace form

\( 14q - 3q^{2} + 4q^{3} + 5q^{4} - 6q^{6} - 2q^{7} - 2q^{9} + O(q^{10}) \) \( 14q - 3q^{2} + 4q^{3} + 5q^{4} - 6q^{6} - 2q^{7} - 2q^{9} - 18q^{10} - 2q^{12} - 4q^{13} + 10q^{14} - 9q^{15} - 3q^{16} + 11q^{17} + 3q^{18} - 6q^{20} - 16q^{21} - 6q^{22} + 3q^{23} - 7q^{25} - 12q^{26} + 22q^{27} + 26q^{28} - 4q^{29} - 28q^{30} - 15q^{31} + 9q^{32} + 27q^{35} - 15q^{36} + 15q^{37} + 16q^{38} + q^{39} - 4q^{40} - 15q^{41} - 14q^{42} + 24q^{44} - 3q^{45} - 30q^{46} + 14q^{48} + 20q^{49} + 24q^{50} + 10q^{51} + 52q^{52} + q^{53} - 9q^{54} - 24q^{55} + 3q^{56} + 21q^{59} + 33q^{60} + 4q^{61} + 38q^{62} - 44q^{63} + 6q^{65} - 43q^{66} - 5q^{68} + 7q^{69} - 18q^{70} + 33q^{71} - 57q^{73} - 33q^{74} + 3q^{75} - 42q^{76} - 10q^{77} + 47q^{78} - 30q^{79} - 26q^{81} + 8q^{82} + 4q^{84} - 3q^{85} + 90q^{86} + 13q^{87} + 10q^{88} + 36q^{89} - 12q^{90} - 17q^{91} - 66q^{92} - 84q^{93} + 28q^{94} + 5q^{95} - 12q^{96} - 12q^{97} - 45q^{98} + O(q^{100}) \)

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.u.a \(2\) \(0.727\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-2\) \(-3\) \(-5\) \(q+(-2+\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
91.2.u.b \(12\) \(0.727\) 12.0.\(\cdots\).1 None \(0\) \(6\) \(3\) \(3\) \(q-\beta _{10}q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{8})q^{3}+\cdots\)