# Properties

 Label 260.1 Level 260 Weight 1 Dimension 18 Nonzero newspaces 6 Newform subspaces 8 Sturm bound 4032 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$260 = 2^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$6$$ Newform subspaces: $$8$$ Sturm bound: $$4032$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(260))$$.

Total New Old
Modular forms 262 86 176
Cusp forms 22 18 4
Eisenstein series 240 68 172

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 18 0 0 0

## Trace form

 $$18 q - 6 q^{8} + O(q^{10})$$ $$18 q - 6 q^{8} - 3 q^{10} - 6 q^{17} - 6 q^{18} - 3 q^{20} - 6 q^{29} - 6 q^{37} - 6 q^{41} - 3 q^{45} + 9 q^{50} + 6 q^{52} + 6 q^{58} - 6 q^{61} + 6 q^{64} - 3 q^{65} + 6 q^{68} + 6 q^{74} + 9 q^{80} + 6 q^{82} - 3 q^{85} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(260))$$

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
260.1.b $$\chi_{260}(131, \cdot)$$ None 0 1
260.1.e $$\chi_{260}(51, \cdot)$$ None 0 1
260.1.g $$\chi_{260}(259, \cdot)$$ 260.1.g.a 1 1
260.1.g.b 1
260.1.h $$\chi_{260}(79, \cdot)$$ None 0 1
260.1.k $$\chi_{260}(109, \cdot)$$ None 0 2
260.1.l $$\chi_{260}(47, \cdot)$$ 260.1.l.a 2 2
260.1.n $$\chi_{260}(77, \cdot)$$ None 0 2
260.1.q $$\chi_{260}(53, \cdot)$$ None 0 2
260.1.s $$\chi_{260}(187, \cdot)$$ 260.1.s.a 2 2
260.1.t $$\chi_{260}(21, \cdot)$$ None 0 2
260.1.v $$\chi_{260}(139, \cdot)$$ None 0 2
260.1.w $$\chi_{260}(179, \cdot)$$ 260.1.w.a 2 2
260.1.w.b 2
260.1.y $$\chi_{260}(231, \cdot)$$ None 0 2
260.1.bb $$\chi_{260}(191, \cdot)$$ None 0 2
260.1.bd $$\chi_{260}(41, \cdot)$$ None 0 4
260.1.be $$\chi_{260}(63, \cdot)$$ 260.1.be.a 4 4
260.1.bh $$\chi_{260}(113, \cdot)$$ None 0 4
260.1.bi $$\chi_{260}(17, \cdot)$$ None 0 4
260.1.bl $$\chi_{260}(7, \cdot)$$ 260.1.bl.a 4 4
260.1.bm $$\chi_{260}(89, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(260))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(260)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 2}$$