## Defining parameters

 Level: $$N$$ = $$1148 = 2^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$6$$ Sturm bound: $$80640$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1148))$$.

Total New Old
Modular forms 1272 424 848
Cusp forms 72 32 40
Eisenstein series 1200 392 808

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 16 0 8 8

## Trace form

 $$32q - 4q^{4} - 2q^{7} - 8q^{9} + O(q^{10})$$ $$32q - 4q^{4} - 2q^{7} - 8q^{9} - 4q^{10} + 4q^{11} - 8q^{13} - 2q^{15} - 12q^{16} - 4q^{23} - 8q^{25} + 4q^{26} - 6q^{29} + 16q^{36} - 2q^{37} - 2q^{39} + 4q^{40} + 16q^{41} - 12q^{42} - 2q^{43} + 8q^{45} - 2q^{49} - 16q^{50} - 4q^{51} - 4q^{52} - 4q^{53} - 10q^{57} + 8q^{64} - 2q^{65} + 12q^{66} - 4q^{77} + 8q^{79} - 20q^{81} + 4q^{82} + 4q^{85} - 4q^{89} + 32q^{90} + 2q^{93} + 2q^{95} - 8q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1148))$$

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
1148.1.b $$\chi_{1148}(657, \cdot)$$ None 0 1
1148.1.e $$\chi_{1148}(575, \cdot)$$ None 0 1
1148.1.g $$\chi_{1148}(573, \cdot)$$ None 0 1
1148.1.h $$\chi_{1148}(491, \cdot)$$ None 0 1
1148.1.j $$\chi_{1148}(155, \cdot)$$ None 0 2
1148.1.m $$\chi_{1148}(237, \cdot)$$ None 0 2
1148.1.o $$\chi_{1148}(163, \cdot)$$ 1148.1.o.a 2 2
1148.1.o.b 2
1148.1.o.c 4
1148.1.o.d 8
1148.1.q $$\chi_{1148}(409, \cdot)$$ None 0 2
1148.1.s $$\chi_{1148}(247, \cdot)$$ None 0 2
1148.1.t $$\chi_{1148}(493, \cdot)$$ None 0 2
1148.1.v $$\chi_{1148}(85, \cdot)$$ None 0 4
1148.1.x $$\chi_{1148}(27, \cdot)$$ None 0 4
1148.1.z $$\chi_{1148}(379, \cdot)$$ None 0 4
1148.1.bc $$\chi_{1148}(461, \cdot)$$ 1148.1.bc.a 8 4
1148.1.bd $$\chi_{1148}(127, \cdot)$$ None 0 4
1148.1.be $$\chi_{1148}(209, \cdot)$$ None 0 4
1148.1.bg $$\chi_{1148}(73, \cdot)$$ None 0 4
1148.1.bj $$\chi_{1148}(319, \cdot)$$ 1148.1.bj.a 8 4
1148.1.bl $$\chi_{1148}(125, \cdot)$$ None 0 8
1148.1.bo $$\chi_{1148}(43, \cdot)$$ None 0 8
1148.1.bq $$\chi_{1148}(3, \cdot)$$ None 0 8
1148.1.bs $$\chi_{1148}(109, \cdot)$$ None 0 8
1148.1.bt $$\chi_{1148}(45, \cdot)$$ None 0 8
1148.1.bv $$\chi_{1148}(23, \cdot)$$ None 0 8
1148.1.bx $$\chi_{1148}(201, \cdot)$$ None 0 8
1148.1.by $$\chi_{1148}(51, \cdot)$$ None 0 8
1148.1.cb $$\chi_{1148}(111, \cdot)$$ None 0 16
1148.1.cd $$\chi_{1148}(29, \cdot)$$ None 0 16
1148.1.ce $$\chi_{1148}(39, \cdot)$$ None 0 16
1148.1.ch $$\chi_{1148}(5, \cdot)$$ None 0 16
1148.1.ci $$\chi_{1148}(53, \cdot)$$ None 0 32
1148.1.ck $$\chi_{1148}(19, \cdot)$$ None 0 32

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1148))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1148)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(164))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(287))$$$$^{\oplus 3}$$