Defining parameters

 Level: $$N$$ = $$1568 = 2^{5} \cdot 7^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$10$$ Newform subspaces: $$13$$ Sturm bound: $$150528$$ Trace bound: $$18$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1568))$$.

Total New Old
Modular forms 2080 536 1544
Cusp forms 160 51 109
Eisenstein series 1920 485 1435

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 43 8 0 0

Trace form

 $$51 q + 2 q^{5} + q^{9} + O(q^{10})$$ $$51 q + 2 q^{5} + q^{9} + 4 q^{16} + 2 q^{17} + 4 q^{18} - 4 q^{22} + 6 q^{23} + q^{25} + 2 q^{33} - 2 q^{37} + 10 q^{43} - 4 q^{44} + 2 q^{53} - 20 q^{57} - 2 q^{61} - 4 q^{67} - 4 q^{69} + 4 q^{71} - 2 q^{73} - 4 q^{74} - 2 q^{79} - 3 q^{81} + 8 q^{85} - 2 q^{89} - 20 q^{92} + 2 q^{93} - 6 q^{99} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1568))$$

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
1568.1.c $$\chi_{1568}(97, \cdot)$$ 1568.1.c.a 4 1
1568.1.d $$\chi_{1568}(1471, \cdot)$$ 1568.1.d.a 2 1
1568.1.d.b 2
1568.1.g $$\chi_{1568}(687, \cdot)$$ 1568.1.g.a 1 1
1568.1.g.b 2
1568.1.h $$\chi_{1568}(881, \cdot)$$ None 0 1
1568.1.k $$\chi_{1568}(295, \cdot)$$ None 0 2
1568.1.l $$\chi_{1568}(489, \cdot)$$ None 0 2
1568.1.n $$\chi_{1568}(913, \cdot)$$ 1568.1.n.a 2 2
1568.1.o $$\chi_{1568}(79, \cdot)$$ 1568.1.o.a 2 2
1568.1.o.b 4
1568.1.r $$\chi_{1568}(863, \cdot)$$ 1568.1.r.a 4 2
1568.1.s $$\chi_{1568}(129, \cdot)$$ 1568.1.s.a 8 2
1568.1.w $$\chi_{1568}(293, \cdot)$$ None 0 4
1568.1.x $$\chi_{1568}(99, \cdot)$$ 1568.1.x.a 4 4
1568.1.z $$\chi_{1568}(263, \cdot)$$ None 0 4
1568.1.bc $$\chi_{1568}(313, \cdot)$$ None 0 4
1568.1.bd $$\chi_{1568}(209, \cdot)$$ None 0 6
1568.1.be $$\chi_{1568}(15, \cdot)$$ None 0 6
1568.1.bh $$\chi_{1568}(127, \cdot)$$ None 0 6
1568.1.bi $$\chi_{1568}(321, \cdot)$$ None 0 6
1568.1.bl $$\chi_{1568}(117, \cdot)$$ 1568.1.bl.a 8 8
1568.1.bo $$\chi_{1568}(67, \cdot)$$ 1568.1.bo.a 8 8
1568.1.bq $$\chi_{1568}(41, \cdot)$$ None 0 12
1568.1.br $$\chi_{1568}(71, \cdot)$$ None 0 12
1568.1.bu $$\chi_{1568}(33, \cdot)$$ None 0 12
1568.1.bv $$\chi_{1568}(95, \cdot)$$ None 0 12
1568.1.by $$\chi_{1568}(207, \cdot)$$ None 0 12
1568.1.bz $$\chi_{1568}(17, \cdot)$$ None 0 12
1568.1.cb $$\chi_{1568}(43, \cdot)$$ None 0 24
1568.1.cc $$\chi_{1568}(13, \cdot)$$ None 0 24
1568.1.ce $$\chi_{1568}(73, \cdot)$$ None 0 24
1568.1.ch $$\chi_{1568}(23, \cdot)$$ None 0 24
1568.1.ci $$\chi_{1568}(11, \cdot)$$ None 0 48
1568.1.cl $$\chi_{1568}(5, \cdot)$$ None 0 48

Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1568))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1568)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(784))$$$$^{\oplus 2}$$