# 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

# Related objects

## 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

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