# Properties

 Label 133.1.m Level 133 Weight 1 Character orbit m Rep. character $$\chi_{133}(83,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 4 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.m (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 8 8 0
Cusp forms 4 4 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 0 4 0 0

## Trace form

 $$4q - 2q^{2} - 4q^{8} + O(q^{10})$$ $$4q - 2q^{2} - 4q^{8} - 2q^{15} + 2q^{16} + 2q^{21} - 2q^{23} + 2q^{29} + 4q^{30} - 2q^{35} - 4q^{39} + 2q^{42} - 2q^{43} + 4q^{46} - 4q^{49} + 2q^{51} + 2q^{53} - 2q^{57} - 4q^{58} + 4q^{64} + 4q^{65} - 2q^{67} - 2q^{70} + 2q^{71} + 2q^{78} - 2q^{79} + 2q^{81} - 2q^{85} - 2q^{86} + 2q^{91} + 2q^{95} + 2q^{98} + O(q^{100})$$

## 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.m.a $$4$$ $$0.066$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots$$

## Hecke characteristic polynomials

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