## Defining parameters

 Level: $$N$$ = $$140 = 2^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newforms: $$4$$ Sturm bound: $$1152$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(140))$$.

Total New Old
Modular forms 126 38 88
Cusp forms 6 6 0
Eisenstein series 120 32 88

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6q - 2q^{4} - 2q^{5} - 4q^{6} + O(q^{10})$$ $$6q - 2q^{4} - 2q^{5} - 4q^{6} - 2q^{11} + 4q^{14} - 2q^{15} - 2q^{16} + 4q^{20} + 2q^{24} - 6q^{29} + 2q^{30} + 2q^{35} + 2q^{39} - 4q^{41} + 2q^{46} + 2q^{51} - 2q^{54} - 2q^{56} + 2q^{61} + 4q^{64} - 2q^{65} + 4q^{69} - 2q^{70} + 4q^{71} - 2q^{79} - 2q^{80} - 4q^{84} - 2q^{85} + 2q^{86} + 2q^{89} - 2q^{91} - 4q^{94} + 2q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(140))$$

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
140.1.b $$\chi_{140}(71, \cdot)$$ None 0 1
140.1.d $$\chi_{140}(41, \cdot)$$ None 0 1
140.1.f $$\chi_{140}(99, \cdot)$$ None 0 1
140.1.h $$\chi_{140}(69, \cdot)$$ 140.1.h.a 1 1
140.1.h.b 1
140.1.j $$\chi_{140}(27, \cdot)$$ None 0 2
140.1.l $$\chi_{140}(57, \cdot)$$ None 0 2
140.1.n $$\chi_{140}(89, \cdot)$$ None 0 2
140.1.p $$\chi_{140}(39, \cdot)$$ 140.1.p.a 2 2
140.1.p.b 2
140.1.r $$\chi_{140}(61, \cdot)$$ None 0 2
140.1.t $$\chi_{140}(11, \cdot)$$ None 0 2
140.1.v $$\chi_{140}(37, \cdot)$$ None 0 4
140.1.x $$\chi_{140}(3, \cdot)$$ None 0 4