## Defining parameters

 Level: $$N$$ = $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$6$$ Newform subspaces: $$11$$ Sturm bound: $$23328$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(567))$$.

Total New Old
Modular forms 681 302 379
Cusp forms 33 22 11
Eisenstein series 648 280 368

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 22 0 0 0

## Trace form

 $$22q + q^{4} + q^{7} + O(q^{10})$$ $$22q + q^{4} + q^{7} + 2q^{13} + q^{16} - 4q^{19} + q^{25} - 14q^{28} + 2q^{31} - 4q^{37} + 2q^{43} - 12q^{46} - 5q^{49} - 4q^{52} - 4q^{61} - 2q^{64} - 4q^{67} - 4q^{73} - 4q^{76} - 4q^{79} - 4q^{91} + 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(567))$$

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
567.1.b $$\chi_{567}(323, \cdot)$$ None 0 1
567.1.d $$\chi_{567}(244, \cdot)$$ 567.1.d.a 1 1
567.1.d.b 1
567.1.d.c 2
567.1.j $$\chi_{567}(296, \cdot)$$ 567.1.j.a 2 2
567.1.k $$\chi_{567}(460, \cdot)$$ 567.1.k.a 2 2
567.1.l $$\chi_{567}(55, \cdot)$$ 567.1.l.a 2 2
567.1.l.b 2
567.1.l.c 2
567.1.l.d 4
567.1.m $$\chi_{567}(82, \cdot)$$ None 0 2
567.1.n $$\chi_{567}(53, \cdot)$$ 567.1.n.a 2 2
567.1.q $$\chi_{567}(242, \cdot)$$ None 0 2
567.1.r $$\chi_{567}(134, \cdot)$$ None 0 2
567.1.t $$\chi_{567}(136, \cdot)$$ 567.1.t.a 2 2
567.1.x $$\chi_{567}(73, \cdot)$$ None 0 6
567.1.y $$\chi_{567}(118, \cdot)$$ None 0 6
567.1.z $$\chi_{567}(10, \cdot)$$ None 0 6
567.1.bb $$\chi_{567}(8, \cdot)$$ None 0 6
567.1.bc $$\chi_{567}(170, \cdot)$$ None 0 6
567.1.bf $$\chi_{567}(44, \cdot)$$ None 0 6
567.1.bj $$\chi_{567}(11, \cdot)$$ None 0 18
567.1.bk $$\chi_{567}(40, \cdot)$$ None 0 18
567.1.bn $$\chi_{567}(13, \cdot)$$ None 0 18
567.1.bo $$\chi_{567}(31, \cdot)$$ None 0 18
567.1.bp $$\chi_{567}(29, \cdot)$$ None 0 18
567.1.bq $$\chi_{567}(2, \cdot)$$ None 0 18

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(567))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(567)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 2}$$