## Defining parameters

 Level: $$N$$ = $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$1536$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(160))$$.

Total New Old
Modular forms 132 32 100
Cusp forms 4 2 2
Eisenstein series 128 30 98

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

 $$2q + O(q^{10})$$ $$2q - 2q^{13} - 2q^{17} - 2q^{25} + 2q^{37} + 2q^{45} + 2q^{53} + 2q^{65} + 2q^{73} - 2q^{81} - 2q^{85} + 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(160))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
160.1.b $$\chi_{160}(31, \cdot)$$ None 0 1
160.1.e $$\chi_{160}(79, \cdot)$$ None 0 1
160.1.g $$\chi_{160}(111, \cdot)$$ None 0 1
160.1.h $$\chi_{160}(159, \cdot)$$ None 0 1
160.1.i $$\chi_{160}(57, \cdot)$$ None 0 2
160.1.k $$\chi_{160}(39, \cdot)$$ None 0 2
160.1.m $$\chi_{160}(17, \cdot)$$ None 0 2
160.1.p $$\chi_{160}(33, \cdot)$$ 160.1.p.a 2 2
160.1.r $$\chi_{160}(71, \cdot)$$ None 0 2
160.1.t $$\chi_{160}(137, \cdot)$$ None 0 2
160.1.v $$\chi_{160}(13, \cdot)$$ None 0 4
160.1.w $$\chi_{160}(11, \cdot)$$ None 0 4
160.1.y $$\chi_{160}(19, \cdot)$$ None 0 4
160.1.bb $$\chi_{160}(53, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(160))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(160)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

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