## Defining parameters

 Level: $$N$$ = $$108\( 108 = 2^{2} \cdot 3^{3}$$ \) Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$648$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(108))$$.

Total New Old
Modular forms 76 17 59
Cusp forms 1 1 0
Eisenstein series 75 16 59

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

 $$q - q^{7} + O(q^{10})$$ $$q - q^{7} - q^{13} - q^{19} + q^{25} + 2q^{31} - q^{37} + 2q^{43} - q^{61} - q^{67} - q^{73} - q^{79} + q^{91} - q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(108))$$

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
108.1.c $$\chi_{108}(53, \cdot)$$ 108.1.c.a 1 1
108.1.d $$\chi_{108}(55, \cdot)$$ None 0 1
108.1.f $$\chi_{108}(19, \cdot)$$ None 0 2
108.1.g $$\chi_{108}(17, \cdot)$$ None 0 2
108.1.j $$\chi_{108}(7, \cdot)$$ None 0 6
108.1.k $$\chi_{108}(5, \cdot)$$ None 0 6

## Hecke characteristic polynomials

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