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Properties

Label 8085.2
Level 8085
Weight 2
Dimension 1459560
Nonzero newspaces 96
Sturm bound 9031680

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Defining parameters

Level: \( N \) = \( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(9031680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8085))\).

Total New Old
Modular forms 2277120 1470032 807088
Cusp forms 2238721 1459560 779161
Eisenstein series 38399 10472 27927

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8085))\)

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
8085.2.a \(\chi_{8085}(1, \cdot)\) 8085.2.a.a 1 1
8085.2.a.b 1
8085.2.a.c 1
8085.2.a.d 1
8085.2.a.e 1
8085.2.a.f 1
8085.2.a.g 1
8085.2.a.h 1
8085.2.a.i 1
8085.2.a.j 1
8085.2.a.k 1
8085.2.a.l 1
8085.2.a.m 1
8085.2.a.n 1
8085.2.a.o 1
8085.2.a.p 1
8085.2.a.q 1
8085.2.a.r 1
8085.2.a.s 1
8085.2.a.t 1
8085.2.a.u 1
8085.2.a.v 1
8085.2.a.w 1
8085.2.a.x 1
8085.2.a.y 1
8085.2.a.z 1
8085.2.a.ba 2
8085.2.a.bb 2
8085.2.a.bc 2
8085.2.a.bd 2
8085.2.a.be 2
8085.2.a.bf 2
8085.2.a.bg 2
8085.2.a.bh 2
8085.2.a.bi 3
8085.2.a.bj 3
8085.2.a.bk 3
8085.2.a.bl 3
8085.2.a.bm 3
8085.2.a.bn 4
8085.2.a.bo 4
8085.2.a.bp 4
8085.2.a.bq 4
8085.2.a.br 5
8085.2.a.bs 5
8085.2.a.bt 5
8085.2.a.bu 5
8085.2.a.bv 5
8085.2.a.bw 6
8085.2.a.bx 6
8085.2.a.by 6
8085.2.a.bz 6
8085.2.a.ca 7
8085.2.a.cb 7
8085.2.a.cc 7
8085.2.a.cd 7
8085.2.a.ce 8
8085.2.a.cf 8
8085.2.a.cg 9
8085.2.a.ch 9
8085.2.a.ci 10
8085.2.a.cj 10
8085.2.a.ck 10
8085.2.a.cl 10
8085.2.a.cm 10
8085.2.a.cn 10
8085.2.a.co 14
8085.2.a.cp 14
8085.2.c \(\chi_{8085}(6469, \cdot)\) n/a 412 1
8085.2.d \(\chi_{8085}(881, \cdot)\) n/a 536 1
8085.2.f \(\chi_{8085}(1814, \cdot)\) n/a 964 1
8085.2.i \(\chi_{8085}(7006, \cdot)\) n/a 320 1
8085.2.k \(\chi_{8085}(5389, \cdot)\) n/a 480 1
8085.2.l \(\chi_{8085}(3431, \cdot)\) n/a 656 1
8085.2.n \(\chi_{8085}(7349, \cdot)\) n/a 800 1
8085.2.q \(\chi_{8085}(3301, \cdot)\) n/a 536 2
8085.2.s \(\chi_{8085}(4313, \cdot)\) n/a 1640 2
8085.2.t \(\chi_{8085}(3233, \cdot)\) n/a 1888 2
8085.2.v \(\chi_{8085}(3037, \cdot)\) n/a 800 2
8085.2.y \(\chi_{8085}(2353, \cdot)\) n/a 984 2
8085.2.z \(\chi_{8085}(2941, \cdot)\) n/a 1312 4
8085.2.bb \(\chi_{8085}(1451, \cdot)\) n/a 1280 2
8085.2.bc \(\chi_{8085}(2089, \cdot)\) n/a 960 2
8085.2.bg \(\chi_{8085}(1244, \cdot)\) n/a 1600 2
8085.2.bi \(\chi_{8085}(2861, \cdot)\) n/a 1064 2
8085.2.bj \(\chi_{8085}(1684, \cdot)\) n/a 800 2
8085.2.bl \(\chi_{8085}(901, \cdot)\) n/a 640 2
8085.2.bo \(\chi_{8085}(5114, \cdot)\) n/a 1888 2
8085.2.bp \(\chi_{8085}(1156, \cdot)\) n/a 2256 6
8085.2.bs \(\chi_{8085}(2204, \cdot)\) n/a 3776 4
8085.2.bu \(\chi_{8085}(491, \cdot)\) n/a 2624 4
8085.2.bv \(\chi_{8085}(244, \cdot)\) n/a 1920 4
8085.2.bx \(\chi_{8085}(391, \cdot)\) n/a 1280 4
8085.2.ca \(\chi_{8085}(2549, \cdot)\) n/a 3856 4
8085.2.cc \(\chi_{8085}(146, \cdot)\) n/a 2560 4
8085.2.cd \(\chi_{8085}(1324, \cdot)\) n/a 1968 4
8085.2.cf \(\chi_{8085}(373, \cdot)\) n/a 1920 4
8085.2.ci \(\chi_{8085}(1783, \cdot)\) n/a 1600 4
8085.2.ck \(\chi_{8085}(362, \cdot)\) n/a 3776 4
8085.2.cl \(\chi_{8085}(2333, \cdot)\) n/a 3200 4
8085.2.co \(\chi_{8085}(419, \cdot)\) n/a 6720 6
8085.2.cq \(\chi_{8085}(1121, \cdot)\) n/a 5376 6
8085.2.ct \(\chi_{8085}(769, \cdot)\) n/a 4032 6
8085.2.cv \(\chi_{8085}(76, \cdot)\) n/a 2688 6
8085.2.cw \(\chi_{8085}(659, \cdot)\) n/a 8016 6
8085.2.cy \(\chi_{8085}(2036, \cdot)\) n/a 4464 6
8085.2.db \(\chi_{8085}(694, \cdot)\) n/a 3360 6
8085.2.dc \(\chi_{8085}(361, \cdot)\) n/a 2560 8
8085.2.dd \(\chi_{8085}(442, \cdot)\) n/a 3936 8
8085.2.dg \(\chi_{8085}(97, \cdot)\) n/a 3840 8
8085.2.di \(\chi_{8085}(293, \cdot)\) n/a 7552 8
8085.2.dj \(\chi_{8085}(1373, \cdot)\) n/a 7712 8
8085.2.dl \(\chi_{8085}(331, \cdot)\) n/a 4464 12
8085.2.dm \(\chi_{8085}(692, \cdot)\) n/a 16032 12
8085.2.dp \(\chi_{8085}(617, \cdot)\) n/a 13440 12
8085.2.dr \(\chi_{8085}(43, \cdot)\) n/a 8064 12
8085.2.ds \(\chi_{8085}(727, \cdot)\) n/a 6720 12
8085.2.du \(\chi_{8085}(569, \cdot)\) n/a 7552 8
8085.2.dx \(\chi_{8085}(766, \cdot)\) n/a 2560 8
8085.2.dz \(\chi_{8085}(214, \cdot)\) n/a 3840 8
8085.2.ea \(\chi_{8085}(521, \cdot)\) n/a 5120 8
8085.2.ec \(\chi_{8085}(509, \cdot)\) n/a 7552 8
8085.2.eg \(\chi_{8085}(19, \cdot)\) n/a 3840 8
8085.2.eh \(\chi_{8085}(116, \cdot)\) n/a 5120 8
8085.2.ej \(\chi_{8085}(421, \cdot)\) n/a 10752 24
8085.2.el \(\chi_{8085}(494, \cdot)\) n/a 16032 12
8085.2.em \(\chi_{8085}(241, \cdot)\) n/a 5376 12
8085.2.eo \(\chi_{8085}(529, \cdot)\) n/a 6720 12
8085.2.er \(\chi_{8085}(551, \cdot)\) n/a 8976 12
8085.2.et \(\chi_{8085}(89, \cdot)\) n/a 13440 12
8085.2.ev \(\chi_{8085}(439, \cdot)\) n/a 8064 12
8085.2.ey \(\chi_{8085}(296, \cdot)\) n/a 10752 12
8085.2.fa \(\chi_{8085}(422, \cdot)\) n/a 15104 16
8085.2.fb \(\chi_{8085}(68, \cdot)\) n/a 15104 16
8085.2.fd \(\chi_{8085}(313, \cdot)\) n/a 7680 16
8085.2.fg \(\chi_{8085}(508, \cdot)\) n/a 7680 16
8085.2.fh \(\chi_{8085}(64, \cdot)\) n/a 16128 24
8085.2.fk \(\chi_{8085}(251, \cdot)\) n/a 21504 24
8085.2.fm \(\chi_{8085}(29, \cdot)\) n/a 32064 24
8085.2.fn \(\chi_{8085}(601, \cdot)\) n/a 10752 24
8085.2.fp \(\chi_{8085}(139, \cdot)\) n/a 16128 24
8085.2.fs \(\chi_{8085}(281, \cdot)\) n/a 21504 24
8085.2.fu \(\chi_{8085}(104, \cdot)\) n/a 32064 24
8085.2.fx \(\chi_{8085}(397, \cdot)\) n/a 13440 24
8085.2.fy \(\chi_{8085}(142, \cdot)\) n/a 16128 24
8085.2.ga \(\chi_{8085}(23, \cdot)\) n/a 26880 24
8085.2.gd \(\chi_{8085}(593, \cdot)\) n/a 32064 24
8085.2.ge \(\chi_{8085}(16, \cdot)\) n/a 21504 48
8085.2.gg \(\chi_{8085}(202, \cdot)\) n/a 32256 48
8085.2.gh \(\chi_{8085}(127, \cdot)\) n/a 32256 48
8085.2.gj \(\chi_{8085}(92, \cdot)\) n/a 64128 48
8085.2.gm \(\chi_{8085}(62, \cdot)\) n/a 64128 48
8085.2.gn \(\chi_{8085}(326, \cdot)\) n/a 43008 48
8085.2.gq \(\chi_{8085}(94, \cdot)\) n/a 32256 48
8085.2.gs \(\chi_{8085}(59, \cdot)\) n/a 64128 48
8085.2.gu \(\chi_{8085}(26, \cdot)\) n/a 43008 48
8085.2.gx \(\chi_{8085}(4, \cdot)\) n/a 32256 48
8085.2.gz \(\chi_{8085}(61, \cdot)\) n/a 21504 48
8085.2.ha \(\chi_{8085}(74, \cdot)\) n/a 64128 48
8085.2.hc \(\chi_{8085}(17, \cdot)\) n/a 128256 96
8085.2.hf \(\chi_{8085}(53, \cdot)\) n/a 128256 96
8085.2.hh \(\chi_{8085}(172, \cdot)\) n/a 64512 96
8085.2.hi \(\chi_{8085}(82, \cdot)\) n/a 64512 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8085))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8085)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1155))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1617))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2695))\)\(^{\oplus 2}\)