Properties

Label 585.6
Level 585
Weight 6
Dimension 43068
Nonzero newspaces 50
Sturm bound 145152
Trace bound 10

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Defining parameters

Level: \( N \) = \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 50 \)
Sturm bound: \(145152\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(585))\).

Total New Old
Modular forms 61248 43664 17584
Cusp forms 59712 43068 16644
Eisenstein series 1536 596 940

Trace form

\( 43068 q + 4 q^{2} - 80 q^{3} - 104 q^{4} + 228 q^{5} + 572 q^{6} + 136 q^{7} - 5124 q^{8} - 1936 q^{9} + 4606 q^{10} + 7336 q^{11} + 10352 q^{12} + 1642 q^{13} - 9312 q^{14} - 8504 q^{15} - 17408 q^{16}+ \cdots - 1035128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(585))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
585.6.a \(\chi_{585}(1, \cdot)\) 585.6.a.a 1 1
585.6.a.b 1
585.6.a.c 3
585.6.a.d 4
585.6.a.e 4
585.6.a.f 4
585.6.a.g 4
585.6.a.h 4
585.6.a.i 5
585.6.a.j 5
585.6.a.k 6
585.6.a.l 6
585.6.a.m 6
585.6.a.n 7
585.6.a.o 9
585.6.a.p 9
585.6.a.q 11
585.6.a.r 11
585.6.b \(\chi_{585}(181, \cdot)\) n/a 118 1
585.6.c \(\chi_{585}(469, \cdot)\) n/a 150 1
585.6.h \(\chi_{585}(64, \cdot)\) n/a 172 1
585.6.i \(\chi_{585}(196, \cdot)\) n/a 480 2
585.6.j \(\chi_{585}(406, \cdot)\) n/a 232 2
585.6.k \(\chi_{585}(61, \cdot)\) n/a 560 2
585.6.l \(\chi_{585}(16, \cdot)\) n/a 560 2
585.6.n \(\chi_{585}(307, \cdot)\) n/a 346 2
585.6.p \(\chi_{585}(53, \cdot)\) n/a 240 2
585.6.q \(\chi_{585}(44, \cdot)\) n/a 280 2
585.6.r \(\chi_{585}(161, \cdot)\) n/a 192 2
585.6.v \(\chi_{585}(233, \cdot)\) n/a 280 2
585.6.w \(\chi_{585}(73, \cdot)\) n/a 346 2
585.6.ba \(\chi_{585}(121, \cdot)\) n/a 560 2
585.6.bb \(\chi_{585}(139, \cdot)\) n/a 832 2
585.6.be \(\chi_{585}(259, \cdot)\) n/a 832 2
585.6.bf \(\chi_{585}(199, \cdot)\) n/a 344 2
585.6.bk \(\chi_{585}(49, \cdot)\) n/a 832 2
585.6.bl \(\chi_{585}(94, \cdot)\) n/a 832 2
585.6.bm \(\chi_{585}(166, \cdot)\) n/a 560 2
585.6.br \(\chi_{585}(79, \cdot)\) n/a 720 2
585.6.bs \(\chi_{585}(289, \cdot)\) n/a 348 2
585.6.bt \(\chi_{585}(376, \cdot)\) n/a 560 2
585.6.bu \(\chi_{585}(316, \cdot)\) n/a 232 2
585.6.bx \(\chi_{585}(4, \cdot)\) n/a 832 2
585.6.ca \(\chi_{585}(58, \cdot)\) n/a 1664 4
585.6.cc \(\chi_{585}(67, \cdot)\) n/a 1664 4
585.6.cf \(\chi_{585}(163, \cdot)\) n/a 692 4
585.6.cg \(\chi_{585}(187, \cdot)\) n/a 1664 4
585.6.ci \(\chi_{585}(113, \cdot)\) n/a 1664 4
585.6.cm \(\chi_{585}(11, \cdot)\) n/a 1120 4
585.6.cn \(\chi_{585}(59, \cdot)\) n/a 1664 4
585.6.co \(\chi_{585}(212, \cdot)\) n/a 1664 4
585.6.cr \(\chi_{585}(23, \cdot)\) n/a 1664 4
585.6.cs \(\chi_{585}(38, \cdot)\) n/a 1664 4
585.6.cv \(\chi_{585}(17, \cdot)\) n/a 560 4
585.6.cw \(\chi_{585}(71, \cdot)\) n/a 368 4
585.6.cx \(\chi_{585}(89, \cdot)\) n/a 560 4
585.6.dc \(\chi_{585}(164, \cdot)\) n/a 1664 4
585.6.dd \(\chi_{585}(41, \cdot)\) n/a 1120 4
585.6.de \(\chi_{585}(254, \cdot)\) n/a 1664 4
585.6.df \(\chi_{585}(86, \cdot)\) n/a 1120 4
585.6.dj \(\chi_{585}(92, \cdot)\) n/a 1440 4
585.6.dk \(\chi_{585}(68, \cdot)\) n/a 1664 4
585.6.dn \(\chi_{585}(107, \cdot)\) n/a 560 4
585.6.dp \(\chi_{585}(28, \cdot)\) n/a 692 4
585.6.dq \(\chi_{585}(112, \cdot)\) n/a 1664 4
585.6.dt \(\chi_{585}(7, \cdot)\) n/a 1664 4
585.6.dv \(\chi_{585}(292, \cdot)\) n/a 1664 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(585))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(585)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 1}\)