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Properties

Label 131.2.a
Level $131$
Weight $2$
Character orbit 131.a
Rep. character $\chi_{131}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(131))\) into newform subspaces

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