Properties

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

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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

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