# Properties

 Label 585.1 Level 585 Weight 1 Dimension 8 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 24192 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$24192$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(585))$$.

Total New Old
Modular forms 792 304 488
Cusp forms 24 8 16
Eisenstein series 768 296 472

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

 $$8 q + O(q^{10})$$ $$8 q - 8 q^{10} - 8 q^{16} + 8 q^{22} + 8 q^{40} - 8 q^{43} - 8 q^{52} - 8 q^{82} + 16 q^{88} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(585))$$

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
585.1.d $$\chi_{585}(521, \cdot)$$ None 0 1
585.1.e $$\chi_{585}(584, \cdot)$$ None 0 1
585.1.f $$\chi_{585}(404, \cdot)$$ None 0 1
585.1.g $$\chi_{585}(116, \cdot)$$ None 0 1
585.1.m $$\chi_{585}(8, \cdot)$$ None 0 2
585.1.o $$\chi_{585}(298, \cdot)$$ 585.1.o.a 8 2
585.1.s $$\chi_{585}(226, \cdot)$$ None 0 2
585.1.t $$\chi_{585}(109, \cdot)$$ None 0 2
585.1.u $$\chi_{585}(118, \cdot)$$ None 0 2
585.1.x $$\chi_{585}(242, \cdot)$$ None 0 2
585.1.y $$\chi_{585}(146, \cdot)$$ None 0 2
585.1.z $$\chi_{585}(329, \cdot)$$ None 0 2
585.1.bc $$\chi_{585}(56, \cdot)$$ None 0 2
585.1.bd $$\chi_{585}(74, \cdot)$$ None 0 2
585.1.bg $$\chi_{585}(251, \cdot)$$ None 0 2
585.1.bh $$\chi_{585}(311, \cdot)$$ None 0 2
585.1.bi $$\chi_{585}(224, \cdot)$$ None 0 2
585.1.bj $$\chi_{585}(14, \cdot)$$ None 0 2
585.1.bn $$\chi_{585}(134, \cdot)$$ None 0 2
585.1.bo $$\chi_{585}(194, \cdot)$$ None 0 2
585.1.bp $$\chi_{585}(341, \cdot)$$ None 0 2
585.1.bq $$\chi_{585}(131, \cdot)$$ None 0 2
585.1.bv $$\chi_{585}(374, \cdot)$$ None 0 2
585.1.bw $$\chi_{585}(191, \cdot)$$ None 0 2
585.1.by $$\chi_{585}(29, \cdot)$$ None 0 2
585.1.bz $$\chi_{585}(101, \cdot)$$ None 0 2
585.1.cb $$\chi_{585}(2, \cdot)$$ None 0 4
585.1.cd $$\chi_{585}(47, \cdot)$$ None 0 4
585.1.ce $$\chi_{585}(188, \cdot)$$ None 0 4
585.1.ch $$\chi_{585}(137, \cdot)$$ None 0 4
585.1.cj $$\chi_{585}(88, \cdot)$$ None 0 4
585.1.ck $$\chi_{585}(319, \cdot)$$ None 0 4
585.1.cl $$\chi_{585}(106, \cdot)$$ None 0 4
585.1.cp $$\chi_{585}(22, \cdot)$$ None 0 4
585.1.cq $$\chi_{585}(172, \cdot)$$ None 0 4
585.1.ct $$\chi_{585}(157, \cdot)$$ None 0 4
585.1.cu $$\chi_{585}(178, \cdot)$$ None 0 4
585.1.cy $$\chi_{585}(31, \cdot)$$ None 0 4
585.1.cz $$\chi_{585}(124, \cdot)$$ None 0 4
585.1.da $$\chi_{585}(76, \cdot)$$ None 0 4
585.1.db $$\chi_{585}(34, \cdot)$$ None 0 4
585.1.dg $$\chi_{585}(19, \cdot)$$ None 0 4
585.1.dh $$\chi_{585}(46, \cdot)$$ None 0 4
585.1.di $$\chi_{585}(82, \cdot)$$ None 0 4
585.1.dl $$\chi_{585}(43, \cdot)$$ None 0 4
585.1.dm $$\chi_{585}(103, \cdot)$$ None 0 4
585.1.do $$\chi_{585}(227, \cdot)$$ None 0 4
585.1.dr $$\chi_{585}(122, \cdot)$$ None 0 4
585.1.ds $$\chi_{585}(98, \cdot)$$ None 0 4
585.1.du $$\chi_{585}(353, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(585))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(585)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 2}$$