# Properties

 Label 80.1.h Level 80 Weight 1 Character orbit h Rep. character $$\chi_{80}(79,\cdot)$$ Character field $$\Q$$ Dimension 1 Newform subspaces 1 Sturm bound 12 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$80 = 2^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 80.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(80, [\chi])$$.

Total New Old
Modular forms 7 1 6
Cusp forms 1 1 0
Eisenstein series 6 0 6

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q - q^{5} - q^{9} + O(q^{10})$$ $$q - q^{5} - q^{9} + q^{25} + 2q^{29} - 2q^{41} + q^{45} - q^{49} - 2q^{61} + q^{81} + 2q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(80, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
80.1.h.a $$1$$ $$0.040$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$-1$$ $$0$$ $$q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots$$

## Hecke characteristic polynomials

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