# Properties

 Label 119.1.d Level 119 Weight 1 Character orbit d Rep. character $$\chi_{119}(118,\cdot)$$ Character field $$\Q$$ Dimension 4 Newform subspaces 2 Sturm bound 12 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$119 = 7 \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 119.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$119$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$12$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(119, [\chi])$$.

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

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4q - 2q^{2} + 2q^{4} - 4q^{8} + 2q^{9} + O(q^{10})$$ $$4q - 2q^{2} + 2q^{4} - 4q^{8} + 2q^{9} - 4q^{15} - 6q^{18} - 2q^{21} + 2q^{25} + 2q^{30} + 4q^{32} - 2q^{35} + 6q^{36} + 6q^{42} - 2q^{43} + 4q^{49} + 4q^{50} - 2q^{51} - 2q^{53} - 2q^{60} - 2q^{64} - 2q^{67} - 4q^{70} - 2q^{72} - 6q^{84} - 2q^{85} + 6q^{86} - 4q^{93} - 2q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(119, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
119.1.d.a $$2$$ $$0.059$$ $$\Q(\sqrt{5})$$ $$D_{5}$$ $$\Q(\sqrt{-119})$$ None $$-1$$ $$-1$$ $$-1$$ $$2$$ $$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$$
119.1.d.b $$2$$ $$0.059$$ $$\Q(\sqrt{5})$$ $$D_{5}$$ $$\Q(\sqrt{-119})$$ None $$-1$$ $$1$$ $$1$$ $$-2$$ $$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots$$

## Hecke characteristic polynomials

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