# Properties

 Label 225.1 Level 225 Weight 1 Dimension 2 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 3600 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$225\( 225 = 3^{2} \cdot 5^{2}$$ \) Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$3600$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(225))$$.

Total New Old
Modular forms 226 94 132
Cusp forms 2 2 0
Eisenstein series 224 92 132

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

 $$2q + O(q^{10})$$ $$2q - 2q^{16} - 4q^{31} + 4q^{61} + 4q^{76} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(225))$$

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
225.1.c $$\chi_{225}(26, \cdot)$$ None 0 1
225.1.d $$\chi_{225}(224, \cdot)$$ None 0 1
225.1.g $$\chi_{225}(82, \cdot)$$ 225.1.g.a 2 2
225.1.i $$\chi_{225}(74, \cdot)$$ None 0 2
225.1.j $$\chi_{225}(101, \cdot)$$ None 0 2
225.1.l $$\chi_{225}(44, \cdot)$$ None 0 4
225.1.n $$\chi_{225}(71, \cdot)$$ None 0 4
225.1.o $$\chi_{225}(7, \cdot)$$ None 0 4
225.1.r $$\chi_{225}(28, \cdot)$$ None 0 8
225.1.t $$\chi_{225}(11, \cdot)$$ None 0 8
225.1.v $$\chi_{225}(14, \cdot)$$ None 0 8
225.1.x $$\chi_{225}(13, \cdot)$$ None 0 16

## Hecke characteristic polynomials

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