## Defining parameters

 Level: $$N$$ = $$204 = 2^{2} \cdot 3 \cdot 17$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$2$$ Sturm bound: $$2304$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(204))$$.

Total New Old
Modular forms 168 34 134
Cusp forms 8 2 6
Eisenstein series 160 32 128

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

 $$2q + 2q^{9} + O(q^{10})$$ $$2q + 2q^{9} - 2q^{13} - 2q^{15} - 2q^{19} - 2q^{33} - 2q^{43} + 2q^{49} + 2q^{51} + 2q^{55} + 4q^{67} - 2q^{69} + 2q^{81} - 2q^{85} + 4q^{87} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(204))$$

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
204.1.d $$\chi_{204}(137, \cdot)$$ None 0 1
204.1.e $$\chi_{204}(67, \cdot)$$ None 0 1
204.1.f $$\chi_{204}(103, \cdot)$$ None 0 1
204.1.g $$\chi_{204}(101, \cdot)$$ 204.1.g.a 1 1
204.1.g.b 1
204.1.i $$\chi_{204}(89, \cdot)$$ None 0 2
204.1.k $$\chi_{204}(55, \cdot)$$ None 0 2
204.1.m $$\chi_{204}(53, \cdot)$$ None 0 4
204.1.n $$\chi_{204}(19, \cdot)$$ None 0 4
204.1.s $$\chi_{204}(37, \cdot)$$ None 0 8
204.1.t $$\chi_{204}(11, \cdot)$$ None 0 8

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(204))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(204)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

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