Properties

Label 91.2.a
Level $91$
Weight $2$
Character orbit 91.a
Rep. character $\chi_{91}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $4$
Sturm bound $18$
Trace bound $2$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(18\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(91))\).

Total New Old
Modular forms 10 7 3
Cusp forms 7 7 0
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(5\)

Trace form

\( 7q - q^{2} - 4q^{3} + 3q^{4} + 2q^{5} - q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 7q - q^{2} - 4q^{3} + 3q^{4} + 2q^{5} - q^{7} + 3q^{8} + 3q^{9} + 2q^{10} - 4q^{11} - 8q^{12} + q^{13} + q^{14} - 4q^{15} - 9q^{16} + 2q^{17} - 9q^{18} - 12q^{19} - 2q^{20} - 4q^{22} + 10q^{23} - 4q^{24} + 15q^{25} + 3q^{26} - 4q^{27} - 7q^{28} + 16q^{29} + 8q^{30} - 4q^{31} + 15q^{32} - 4q^{33} + 2q^{34} + 4q^{35} - 9q^{36} - 6q^{37} - 8q^{38} - 4q^{39} - 10q^{40} + 2q^{41} - 8q^{42} - 2q^{43} + 22q^{45} - 16q^{46} + 8q^{47} + 12q^{48} + 7q^{49} + q^{50} + 8q^{51} - q^{52} - 16q^{53} + 48q^{54} + 12q^{55} - 3q^{56} + 30q^{58} + 16q^{59} - 20q^{60} - 14q^{61} - 8q^{62} - 5q^{63} - 17q^{64} - 4q^{65} + 12q^{66} - 16q^{67} + 42q^{68} - 20q^{69} + 6q^{70} - 32q^{71} - q^{72} - 22q^{73} + 26q^{74} - 48q^{75} + 16q^{76} + 4q^{77} + 8q^{78} + 2q^{79} - 38q^{80} - 9q^{81} + 14q^{82} + 24q^{83} + 16q^{84} - 8q^{85} - 24q^{86} - 16q^{87} + 36q^{88} + 26q^{89} - 50q^{90} - 3q^{91} - 12q^{92} - 20q^{93} - 20q^{94} + 6q^{95} - 4q^{96} - 6q^{97} - q^{98} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(91))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 13
91.2.a.a \(1\) \(0.727\) \(\Q\) None \(-2\) \(0\) \(-3\) \(-1\) \(+\) \(+\) \(q-2q^{2}+2q^{4}-3q^{5}-q^{7}-3q^{9}+\cdots\)
91.2.a.b \(1\) \(0.727\) \(\Q\) None \(0\) \(-2\) \(-3\) \(1\) \(-\) \(-\) \(q-2q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}+4q^{12}+\cdots\)
91.2.a.c \(2\) \(0.727\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(6\) \(2\) \(-\) \(+\) \(q+\beta q^{2}-\beta q^{3}+(3+\beta )q^{5}-2q^{6}+q^{7}+\cdots\)
91.2.a.d \(3\) \(0.727\) 3.3.316.1 None \(1\) \(-2\) \(2\) \(-3\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)