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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.2.u.a 91.u 91.u $2$ $0.727$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-2\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
91.2.u.b 91.u 91.u $12$ $0.727$ 12.0.\(\cdots\).1 None \(0\) \(6\) \(3\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{10}q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{8})q^{3}+\cdots\)