## Defining parameters

 Level: $$N$$ = $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$3$$ Sturm bound: $$4608$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(280))$$.

Total New Old
Modular forms 310 68 242
Cusp forms 22 8 14
Eisenstein series 288 60 228

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

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

## Trace form

 $$8q - 6q^{4} - 6q^{9} + O(q^{10})$$ $$8q - 6q^{4} - 6q^{9} - 2q^{10} + 2q^{11} + 2q^{14} - 4q^{15} + 2q^{16} + 2q^{19} - 2q^{25} + 2q^{26} - 4q^{30} - 2q^{35} + 8q^{36} + 8q^{39} - 2q^{40} - 4q^{41} + 2q^{44} + 2q^{46} - 4q^{50} - 4q^{59} + 4q^{60} + 6q^{65} + 2q^{74} - 4q^{76} - 6q^{81} - 4q^{89} + 4q^{90} - 4q^{91} + 2q^{94} - 4q^{95} - 4q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(280))$$

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
280.1.c $$\chi_{280}(69, \cdot)$$ 280.1.c.a 4 1
280.1.d $$\chi_{280}(71, \cdot)$$ None 0 1
280.1.f $$\chi_{280}(41, \cdot)$$ None 0 1
280.1.i $$\chi_{280}(99, \cdot)$$ None 0 1
280.1.j $$\chi_{280}(239, \cdot)$$ None 0 1
280.1.m $$\chi_{280}(181, \cdot)$$ None 0 1
280.1.o $$\chi_{280}(211, \cdot)$$ None 0 1
280.1.p $$\chi_{280}(209, \cdot)$$ None 0 1
280.1.r $$\chi_{280}(167, \cdot)$$ None 0 2
280.1.u $$\chi_{280}(197, \cdot)$$ None 0 2
280.1.v $$\chi_{280}(57, \cdot)$$ None 0 2
280.1.y $$\chi_{280}(27, \cdot)$$ None 0 2
280.1.z $$\chi_{280}(11, \cdot)$$ None 0 2
280.1.bb $$\chi_{280}(89, \cdot)$$ None 0 2
280.1.bd $$\chi_{280}(39, \cdot)$$ None 0 2
280.1.be $$\chi_{280}(61, \cdot)$$ None 0 2
280.1.bh $$\chi_{280}(201, \cdot)$$ None 0 2
280.1.bi $$\chi_{280}(179, \cdot)$$ 280.1.bi.a 2 2
280.1.bi.b 2
280.1.bk $$\chi_{280}(229, \cdot)$$ None 0 2
280.1.bn $$\chi_{280}(151, \cdot)$$ None 0 2
280.1.bp $$\chi_{280}(3, \cdot)$$ None 0 4
280.1.bq $$\chi_{280}(137, \cdot)$$ None 0 4
280.1.bt $$\chi_{280}(37, \cdot)$$ None 0 4
280.1.bu $$\chi_{280}(47, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(280))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(280)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 2}$$