Properties

Label 131.1.b
Level 131
Weight 1
Character orbit b
Rep. character \(\chi_{131}(130,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 11
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 131 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 131.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 131 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(131, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 0
Eisenstein series 1 1 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - q^{3} + 2q^{4} - q^{5} - q^{7} + q^{9} + O(q^{10}) \) \( 2q - q^{3} + 2q^{4} - q^{5} - q^{7} + q^{9} - q^{11} - q^{12} - q^{13} - 2q^{15} + 2q^{16} - q^{20} - 2q^{21} + q^{25} - 2q^{27} - q^{28} + 3q^{33} + 3q^{35} + q^{36} + 3q^{39} - q^{41} - q^{43} - q^{44} + 2q^{45} - q^{48} + q^{49} - q^{52} + 4q^{53} - 2q^{55} - q^{59} - 2q^{60} - q^{61} + 2q^{63} + 2q^{64} - 2q^{65} + 2q^{75} - 2q^{77} - q^{80} - 2q^{84} + 4q^{89} - 2q^{91} - 3q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(131, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
131.1.b.a \(2\) \(0.065\) \(\Q(\sqrt{5}) \) \(D_{5}\) \(\Q(\sqrt{-131}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}-\beta q^{7}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$3$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$5$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$7$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$11$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$13$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$17$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$19$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$23$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$29$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$31$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$37$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$41$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$43$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$47$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$53$ \( ( 1 - T )^{4} \)
$59$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$61$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$67$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$71$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$73$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$79$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$83$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$89$ \( ( 1 - T )^{4} \)
$97$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
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