Properties

Label 131.2.a
Level 131
Weight 2
Character orbit a
Rep. character \(\chi_{131}(1,\cdot)\)
Character field \(\Q\)
Dimension 11
Newforms 2
Sturm bound 22
Trace bound 1

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Defining parameters

Level: \( N \) = \( 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 131.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(22\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(131))\).

Total New Old
Modular forms 12 12 0
Cusp forms 11 11 0
Eisenstein series 1 1 0

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

\(131\)Dim.
\(+\)\(1\)
\(-\)\(10\)

Trace form

\( 11q + 14q^{4} + 2q^{5} - 4q^{6} - 6q^{8} + 13q^{9} + O(q^{10}) \) \( 11q + 14q^{4} + 2q^{5} - 4q^{6} - 6q^{8} + 13q^{9} + 2q^{11} - 6q^{12} + 8q^{13} - 6q^{14} + 32q^{16} + 2q^{17} - 24q^{18} - 2q^{19} - 10q^{20} + 10q^{21} - 4q^{22} - 12q^{23} - 36q^{24} + 17q^{25} - 28q^{26} - 6q^{27} - 22q^{28} + 16q^{29} - 52q^{30} + 4q^{31} - 42q^{32} - 27q^{33} - 4q^{34} - 17q^{35} + 20q^{36} + 26q^{37} - 8q^{38} + 7q^{39} + 10q^{40} - 16q^{41} + 2q^{42} + 12q^{43} + 18q^{44} + 25q^{45} + 32q^{46} + 4q^{47} + 10q^{48} + 17q^{49} + 8q^{50} - 22q^{51} + 10q^{52} + 21q^{53} + 12q^{54} - 20q^{55} - 6q^{56} - 2q^{57} - 4q^{59} + 40q^{60} + 36q^{61} + 4q^{62} - 15q^{63} + 44q^{64} - 8q^{65} + 32q^{66} - 16q^{67} + 24q^{68} + 20q^{69} - 30q^{70} + 10q^{71} - 44q^{72} - 10q^{73} + 52q^{74} - 15q^{75} - 16q^{76} - 24q^{77} + 78q^{78} + 16q^{79} + 6q^{80} + 19q^{81} - 20q^{82} - 18q^{83} + 44q^{84} + 8q^{85} - 20q^{86} - 48q^{87} + 60q^{88} + 3q^{89} + 6q^{90} + 2q^{91} - 44q^{92} + 2q^{93} + 16q^{94} - 24q^{95} - 48q^{96} + 16q^{97} + 80q^{98} - 30q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(131))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 131
131.2.a.a \(1\) \(1.046\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) \(+\) \(q-q^{3}-2q^{4}-2q^{5}-q^{7}-2q^{9}+2q^{12}+\cdots\)
131.2.a.b \(10\) \(1.046\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(1\) \(4\) \(1\) \(-\) \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)