Properties

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

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Defining parameters

Level: \( N \) = \( 91 = 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 91.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(91))\) into irreducible Hecke orbits

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 \(1\) \(-2\) \(2\) \(-3\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)