## Defining parameters

 Level: $$N$$ = $$148 = 2^{2} \cdot 37$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$3$$ Sturm bound: $$1368$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(148))$$.

Total New Old
Modular forms 100 44 56
Cusp forms 10 10 0
Eisenstein series 90 34 56

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 2 0

## Trace form

 $$10 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} - q^{8} - q^{9} + O(q^{10})$$ $$10 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} - q^{8} - q^{9} - 2 q^{10} - 2 q^{13} - q^{16} - 4 q^{17} - q^{18} + 2 q^{19} - 2 q^{20} - 2 q^{23} - 3 q^{25} + 7 q^{26} - 4 q^{29} - q^{32} + 2 q^{33} - 2 q^{34} + 8 q^{36} - q^{37} + 7 q^{40} - 2 q^{41} - 2 q^{45} + 2 q^{47} - q^{49} + 6 q^{50} + 2 q^{51} - 2 q^{52} - 2 q^{57} - 2 q^{58} + 7 q^{61} - q^{64} + 5 q^{65} - 2 q^{68} + 2 q^{69} + 2 q^{71} - q^{72} - 2 q^{73} - q^{74} + 2 q^{75} - 2 q^{79} - 2 q^{80} - 3 q^{81} - 2 q^{82} - 2 q^{83} + 5 q^{85} - 2 q^{87} + 5 q^{89} - 2 q^{90} - 2 q^{97} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(148))$$

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
148.1.b $$\chi_{148}(147, \cdot)$$ None 0 1
148.1.c $$\chi_{148}(75, \cdot)$$ None 0 1
148.1.f $$\chi_{148}(105, \cdot)$$ 148.1.f.a 2 2
148.1.i $$\chi_{148}(47, \cdot)$$ 148.1.i.a 2 2
148.1.j $$\chi_{148}(11, \cdot)$$ None 0 2
148.1.m $$\chi_{148}(29, \cdot)$$ None 0 4
148.1.o $$\chi_{148}(3, \cdot)$$ None 0 6
148.1.p $$\chi_{148}(7, \cdot)$$ 148.1.p.a 6 6
148.1.r $$\chi_{148}(5, \cdot)$$ None 0 12