## Defining parameters

 Level: $$N$$ = $$740 = 2^{2} \cdot 5 \cdot 37$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$10$$ Newform subspaces: $$16$$ Sturm bound: $$32832$$ Trace bound: $$8$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(740))$$.

Total New Old
Modular forms 802 274 528
Cusp forms 82 62 20
Eisenstein series 720 212 508

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 58 0 4 0

## Trace form

 $$62q + 4q^{4} + 2q^{5} + 4q^{9} + O(q^{10})$$ $$62q + 4q^{4} + 2q^{5} + 4q^{9} - 4q^{10} - 2q^{15} + 4q^{16} - 8q^{21} + 4q^{25} - 18q^{26} + 4q^{31} - 2q^{35} - 14q^{36} - 13q^{40} - 8q^{41} + 4q^{49} - 9q^{50} + 2q^{55} - 22q^{61} + 4q^{64} - 9q^{65} - 4q^{71} - 4q^{74} - 4q^{75} + 4q^{79} - 8q^{81} - 8q^{84} - 9q^{85} - 22q^{89} - 4q^{90} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(740))$$

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
740.1.b $$\chi_{740}(591, \cdot)$$ None 0 1
740.1.c $$\chi_{740}(371, \cdot)$$ None 0 1
740.1.f $$\chi_{740}(519, \cdot)$$ None 0 1
740.1.g $$\chi_{740}(739, \cdot)$$ 740.1.g.a 1 1
740.1.g.b 1
740.1.g.c 2
740.1.g.d 2
740.1.j $$\chi_{740}(401, \cdot)$$ None 0 2
740.1.p $$\chi_{740}(43, \cdot)$$ 740.1.p.a 2 2
740.1.q $$\chi_{740}(297, \cdot)$$ None 0 2
740.1.r $$\chi_{740}(73, \cdot)$$ None 0 2
740.1.s $$\chi_{740}(487, \cdot)$$ 740.1.s.a 2 2
740.1.t $$\chi_{740}(549, \cdot)$$ 740.1.t.a 2 2
740.1.t.b 2
740.1.v $$\chi_{740}(159, \cdot)$$ 740.1.v.a 2 2
740.1.v.b 2
740.1.w $$\chi_{740}(359, \cdot)$$ None 0 2
740.1.y $$\chi_{740}(211, \cdot)$$ None 0 2
740.1.z $$\chi_{740}(11, \cdot)$$ None 0 2
740.1.bd $$\chi_{740}(29, \cdot)$$ None 0 4
740.1.bj $$\chi_{740}(103, \cdot)$$ 740.1.bj.a 4 4
740.1.bk $$\chi_{740}(233, \cdot)$$ None 0 4
740.1.bl $$\chi_{740}(137, \cdot)$$ None 0 4
740.1.bm $$\chi_{740}(23, \cdot)$$ 740.1.bm.a 4 4
740.1.bn $$\chi_{740}(341, \cdot)$$ None 0 4
740.1.bs $$\chi_{740}(219, \cdot)$$ None 0 6
740.1.bt $$\chi_{740}(151, \cdot)$$ None 0 6
740.1.bu $$\chi_{740}(99, \cdot)$$ 740.1.bu.a 6 6
740.1.bu.b 6
740.1.bv $$\chi_{740}(71, \cdot)$$ None 0 6
740.1.bw $$\chi_{740}(183, \cdot)$$ 740.1.bw.a 12 12
740.1.by $$\chi_{740}(77, \cdot)$$ None 0 12
740.1.bz $$\chi_{740}(33, \cdot)$$ None 0 12
740.1.cb $$\chi_{740}(87, \cdot)$$ 740.1.cb.a 12 12
740.1.cd $$\chi_{740}(69, \cdot)$$ None 0 12
740.1.cg $$\chi_{740}(61, \cdot)$$ None 0 12

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(740))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(740)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(148))$$$$^{\oplus 2}$$