# Properties

 Label 133.1.r Level 133 Weight 1 Character orbit r Rep. character $$\chi_{133}(18,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 2 Newform subspaces 1 Sturm bound 13 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$133 = 7 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 133.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$133$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$13$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(133, [\chi])$$.

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 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

 $$2q - q^{4} + q^{5} - q^{7} - q^{9} + O(q^{10})$$ $$2q - q^{4} + q^{5} - q^{7} - q^{9} + q^{11} - q^{16} - 2q^{17} - q^{19} - 2q^{20} + q^{23} + 2q^{28} + q^{35} + 2q^{36} - 2q^{43} + q^{44} + q^{45} + q^{47} - q^{49} + 2q^{55} + q^{61} - q^{63} + 2q^{64} - 2q^{68} + q^{73} + 2q^{76} - 2q^{77} + q^{80} - q^{81} - 2q^{83} - 4q^{85} - 2q^{92} + q^{95} - 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(133, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
133.1.r.a $$2$$ $$0.066$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$-1$$ $$q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$$

## Hecke characteristic polynomials

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