Defining parameters

 Level: $$N$$ = $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newforms: $$1$$ 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

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

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