Properties

Label 91.2.e
Level $91$
Weight $2$
Character orbit 91.e
Rep. character $\chi_{91}(53,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $3$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
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 24 16 8
Cusp forms 16 16 0
Eisenstein series 8 0 8

Trace form

\( 16q - 2q^{2} - 10q^{4} - 2q^{5} - 6q^{7} - 4q^{9} + O(q^{10}) \) \( 16q - 2q^{2} - 10q^{4} - 2q^{5} - 6q^{7} - 4q^{9} + 10q^{10} - 2q^{11} + 10q^{12} + 4q^{13} - 10q^{14} - 20q^{15} - 22q^{16} + 4q^{17} - 8q^{19} + 32q^{20} + 2q^{21} + 28q^{22} + 8q^{23} - 20q^{24} - 4q^{25} - 6q^{26} + 30q^{28} - 16q^{29} - 2q^{30} - 4q^{31} - 12q^{32} - 8q^{33} - 32q^{34} - 4q^{35} + 32q^{36} - 8q^{37} + 26q^{38} - 8q^{40} + 28q^{41} + 32q^{42} - 24q^{43} + 6q^{44} + 32q^{45} - 20q^{46} - 2q^{47} - 76q^{48} - 20q^{49} + 8q^{50} + 28q^{51} - 6q^{52} - 8q^{53} - 18q^{54} - 32q^{57} + 42q^{58} - 10q^{59} + 44q^{60} + 12q^{61} - 76q^{62} + 40q^{63} + 40q^{64} - 2q^{65} - 6q^{66} - 4q^{67} + 18q^{68} + 56q^{69} + 54q^{70} + 20q^{71} + 22q^{72} - 22q^{73} + 34q^{74} + 20q^{75} + 48q^{76} - 52q^{77} - 20q^{78} - 4q^{79} - 70q^{80} + 32q^{81} - 44q^{82} + 12q^{83} - 98q^{84} - 4q^{85} - 54q^{86} + 28q^{87} - 24q^{88} + 4q^{89} - 88q^{90} + 8q^{91} - 12q^{92} - 18q^{93} - 46q^{94} + 12q^{95} + 22q^{96} - 68q^{97} + 34q^{98} + 16q^{99} + O(q^{100}) \)

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.e.a \(2\) \(0.727\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
91.2.e.b \(4\) \(0.727\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(3\) \(0\) \(0\) \(-8\) \(q+(1+\beta _{1}+\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots\)
91.2.e.c \(10\) \(0.727\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(-2\) \(1\) \(q+(\beta _{1}-\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots\)