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Properties

Label 8512.2
Level 8512
Weight 2
Dimension 1181956
Nonzero newspaces 128
Sturm bound 8847360

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Defining parameters

Level: \( N \) = \( 8512 = 2^{6} \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 128 \)
Sturm bound: \(8847360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8512))\).

Total New Old
Modular forms 2227392 1189436 1037956
Cusp forms 2196289 1181956 1014333
Eisenstein series 31103 7480 23623

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8512))\)

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
8512.2.a \(\chi_{8512}(1, \cdot)\) 8512.2.a.a 1 1
8512.2.a.b 1
8512.2.a.c 1
8512.2.a.d 1
8512.2.a.e 2
8512.2.a.f 2
8512.2.a.g 2
8512.2.a.h 2
8512.2.a.i 2
8512.2.a.j 2
8512.2.a.k 2
8512.2.a.l 2
8512.2.a.m 2
8512.2.a.n 2
8512.2.a.o 2
8512.2.a.p 2
8512.2.a.q 2
8512.2.a.r 2
8512.2.a.s 2
8512.2.a.t 2
8512.2.a.u 2
8512.2.a.v 2
8512.2.a.w 2
8512.2.a.x 2
8512.2.a.y 2
8512.2.a.z 2
8512.2.a.ba 2
8512.2.a.bb 2
8512.2.a.bc 2
8512.2.a.bd 2
8512.2.a.be 2
8512.2.a.bf 2
8512.2.a.bg 2
8512.2.a.bh 2
8512.2.a.bi 3
8512.2.a.bj 3
8512.2.a.bk 3
8512.2.a.bl 3
8512.2.a.bm 3
8512.2.a.bn 3
8512.2.a.bo 3
8512.2.a.bp 3
8512.2.a.bq 4
8512.2.a.br 4
8512.2.a.bs 4
8512.2.a.bt 4
8512.2.a.bu 4
8512.2.a.bv 4
8512.2.a.bw 5
8512.2.a.bx 5
8512.2.a.by 5
8512.2.a.bz 5
8512.2.a.ca 6
8512.2.a.cb 6
8512.2.a.cc 6
8512.2.a.cd 6
8512.2.a.ce 6
8512.2.a.cf 6
8512.2.a.cg 7
8512.2.a.ch 7
8512.2.a.ci 7
8512.2.a.cj 7
8512.2.a.ck 10
8512.2.a.cl 10
8512.2.b \(\chi_{8512}(4257, \cdot)\) n/a 216 1
8512.2.e \(\chi_{8512}(3039, \cdot)\) n/a 240 1
8512.2.f \(\chi_{8512}(7713, \cdot)\) n/a 320 1
8512.2.i \(\chi_{8512}(2015, \cdot)\) n/a 288 1
8512.2.j \(\chi_{8512}(6271, \cdot)\) n/a 288 1
8512.2.m \(\chi_{8512}(3457, \cdot)\) n/a 316 1
8512.2.n \(\chi_{8512}(7295, \cdot)\) n/a 240 1
8512.2.q \(\chi_{8512}(2433, \cdot)\) n/a 576 2
8512.2.r \(\chi_{8512}(1793, \cdot)\) n/a 480 2
8512.2.s \(\chi_{8512}(5441, \cdot)\) n/a 632 2
8512.2.t \(\chi_{8512}(961, \cdot)\) n/a 632 2
8512.2.u \(\chi_{8512}(1329, \cdot)\) n/a 632 2
8512.2.v \(\chi_{8512}(4143, \cdot)\) n/a 576 2
8512.2.ba \(\chi_{8512}(2129, \cdot)\) n/a 432 2
8512.2.bb \(\chi_{8512}(911, \cdot)\) n/a 480 2
8512.2.bc \(\chi_{8512}(1375, \cdot)\) n/a 640 2
8512.2.bf \(\chi_{8512}(3489, \cdot)\) n/a 640 2
8512.2.bg \(\chi_{8512}(863, \cdot)\) n/a 640 2
8512.2.bj \(\chi_{8512}(5217, \cdot)\) n/a 640 2
8512.2.bk \(\chi_{8512}(3713, \cdot)\) n/a 632 2
8512.2.bn \(\chi_{8512}(1151, \cdot)\) n/a 632 2
8512.2.bp \(\chi_{8512}(1471, \cdot)\) n/a 480 2
8512.2.br \(\chi_{8512}(1215, \cdot)\) n/a 632 2
8512.2.bv \(\chi_{8512}(3583, \cdot)\) n/a 632 2
8512.2.bx \(\chi_{8512}(1025, \cdot)\) n/a 632 2
8512.2.by \(\chi_{8512}(2623, \cdot)\) n/a 576 2
8512.2.ca \(\chi_{8512}(1665, \cdot)\) n/a 632 2
8512.2.ce \(\chi_{8512}(639, \cdot)\) n/a 632 2
8512.2.cf \(\chi_{8512}(4895, \cdot)\) n/a 640 2
8512.2.ci \(\chi_{8512}(1185, \cdot)\) n/a 640 2
8512.2.ck \(\chi_{8512}(1889, \cdot)\) n/a 640 2
8512.2.cm \(\chi_{8512}(6879, \cdot)\) n/a 576 2
8512.2.cn \(\chi_{8512}(4065, \cdot)\) n/a 640 2
8512.2.cp \(\chi_{8512}(3807, \cdot)\) n/a 640 2
8512.2.cs \(\chi_{8512}(1569, \cdot)\) n/a 480 2
8512.2.cu \(\chi_{8512}(5471, \cdot)\) n/a 640 2
8512.2.cv \(\chi_{8512}(6689, \cdot)\) n/a 576 2
8512.2.cx \(\chi_{8512}(1247, \cdot)\) n/a 480 2
8512.2.cz \(\chi_{8512}(159, \cdot)\) n/a 640 2
8512.2.dc \(\chi_{8512}(2273, \cdot)\) n/a 640 2
8512.2.df \(\chi_{8512}(5119, \cdot)\) n/a 632 2
8512.2.dg \(\chi_{8512}(2497, \cdot)\) n/a 632 2
8512.2.dj \(\chi_{8512}(5631, \cdot)\) n/a 632 2
8512.2.dk \(\chi_{8512}(1975, \cdot)\) None 0 4
8512.2.dl \(\chi_{8512}(1065, \cdot)\) None 0 4
8512.2.dq \(\chi_{8512}(951, \cdot)\) None 0 4
8512.2.dr \(\chi_{8512}(265, \cdot)\) None 0 4
8512.2.ds \(\chi_{8512}(897, \cdot)\) n/a 1440 6
8512.2.dt \(\chi_{8512}(1537, \cdot)\) n/a 1896 6
8512.2.du \(\chi_{8512}(1089, \cdot)\) n/a 1896 6
8512.2.dx \(\chi_{8512}(2097, \cdot)\) n/a 1264 4
8512.2.dy \(\chi_{8512}(1551, \cdot)\) n/a 1264 4
8512.2.dz \(\chi_{8512}(369, \cdot)\) n/a 1264 4
8512.2.ea \(\chi_{8512}(2063, \cdot)\) n/a 1264 4
8512.2.ef \(\chi_{8512}(495, \cdot)\) n/a 1152 4
8512.2.eg \(\chi_{8512}(1937, \cdot)\) n/a 1264 4
8512.2.eh \(\chi_{8512}(1775, \cdot)\) n/a 1264 4
8512.2.ei \(\chi_{8512}(3375, \cdot)\) n/a 960 4
8512.2.ej \(\chi_{8512}(1873, \cdot)\) n/a 1264 4
8512.2.ek \(\chi_{8512}(3697, \cdot)\) n/a 960 4
8512.2.et \(\chi_{8512}(2287, \cdot)\) n/a 1264 4
8512.2.eu \(\chi_{8512}(1455, \cdot)\) n/a 1264 4
8512.2.ev \(\chi_{8512}(145, \cdot)\) n/a 1264 4
8512.2.ew \(\chi_{8512}(3793, \cdot)\) n/a 1264 4
8512.2.ex \(\chi_{8512}(303, \cdot)\) n/a 1264 4
8512.2.ey \(\chi_{8512}(305, \cdot)\) n/a 1152 4
8512.2.fb \(\chi_{8512}(797, \cdot)\) n/a 10208 8
8512.2.fc \(\chi_{8512}(533, \cdot)\) n/a 6912 8
8512.2.fd \(\chi_{8512}(379, \cdot)\) n/a 7680 8
8512.2.fe \(\chi_{8512}(419, \cdot)\) n/a 9216 8
8512.2.fj \(\chi_{8512}(1727, \cdot)\) n/a 1896 6
8512.2.fk \(\chi_{8512}(319, \cdot)\) n/a 1896 6
8512.2.fn \(\chi_{8512}(33, \cdot)\) n/a 1920 6
8512.2.fo \(\chi_{8512}(3425, \cdot)\) n/a 1920 6
8512.2.ft \(\chi_{8512}(2561, \cdot)\) n/a 1896 6
8512.2.fw \(\chi_{8512}(257, \cdot)\) n/a 1896 6
8512.2.fz \(\chi_{8512}(671, \cdot)\) n/a 1920 6
8512.2.ga \(\chi_{8512}(2143, \cdot)\) n/a 1440 6
8512.2.gd \(\chi_{8512}(991, \cdot)\) n/a 1920 6
8512.2.ge \(\chi_{8512}(3615, \cdot)\) n/a 1920 6
8512.2.gh \(\chi_{8512}(127, \cdot)\) n/a 1440 6
8512.2.gi \(\chi_{8512}(1791, \cdot)\) n/a 1896 6
8512.2.gl \(\chi_{8512}(1279, \cdot)\) n/a 1896 6
8512.2.gm \(\chi_{8512}(1535, \cdot)\) n/a 1896 6
8512.2.gp \(\chi_{8512}(225, \cdot)\) n/a 1440 6
8512.2.gq \(\chi_{8512}(97, \cdot)\) n/a 1920 6
8512.2.gt \(\chi_{8512}(801, \cdot)\) n/a 1920 6
8512.2.gu \(\chi_{8512}(289, \cdot)\) n/a 1920 6
8512.2.gv \(\chi_{8512}(129, \cdot)\) n/a 1896 6
8512.2.gy \(\chi_{8512}(2207, \cdot)\) n/a 1920 6
8512.2.gz \(\chi_{8512}(479, \cdot)\) n/a 1920 6
8512.2.he \(\chi_{8512}(457, \cdot)\) None 0 8
8512.2.hf \(\chi_{8512}(151, \cdot)\) None 0 8
8512.2.hi \(\chi_{8512}(87, \cdot)\) None 0 8
8512.2.hj \(\chi_{8512}(521, \cdot)\) None 0 8
8512.2.hk \(\chi_{8512}(601, \cdot)\) None 0 8
8512.2.hl \(\chi_{8512}(391, \cdot)\) None 0 8
8512.2.hq \(\chi_{8512}(297, \cdot)\) None 0 8
8512.2.hr \(\chi_{8512}(311, \cdot)\) None 0 8
8512.2.hs \(\chi_{8512}(1033, \cdot)\) None 0 8
8512.2.ht \(\chi_{8512}(487, \cdot)\) None 0 8
8512.2.hy \(\chi_{8512}(711, \cdot)\) None 0 8
8512.2.hz \(\chi_{8512}(121, \cdot)\) None 0 8
8512.2.ia \(\chi_{8512}(505, \cdot)\) None 0 8
8512.2.ib \(\chi_{8512}(183, \cdot)\) None 0 8
8512.2.ie \(\chi_{8512}(873, \cdot)\) None 0 8
8512.2.if \(\chi_{8512}(647, \cdot)\) None 0 8
8512.2.im \(\chi_{8512}(785, \cdot)\) n/a 2880 12
8512.2.in \(\chi_{8512}(433, \cdot)\) n/a 3792 12
8512.2.io \(\chi_{8512}(271, \cdot)\) n/a 3792 12
8512.2.ip \(\chi_{8512}(79, \cdot)\) n/a 3792 12
8512.2.iq \(\chi_{8512}(625, \cdot)\) n/a 3792 12
8512.2.ir \(\chi_{8512}(241, \cdot)\) n/a 3792 12
8512.2.is \(\chi_{8512}(111, \cdot)\) n/a 3792 12
8512.2.it \(\chi_{8512}(15, \cdot)\) n/a 2880 12
8512.2.jc \(\chi_{8512}(751, \cdot)\) n/a 3792 12
8512.2.jd \(\chi_{8512}(47, \cdot)\) n/a 3792 12
8512.2.je \(\chi_{8512}(1041, \cdot)\) n/a 3792 12
8512.2.jf \(\chi_{8512}(81, \cdot)\) n/a 3792 12
8512.2.jg \(\chi_{8512}(715, \cdot)\) n/a 15360 16
8512.2.jh \(\chi_{8512}(83, \cdot)\) n/a 20416 16
8512.2.ji \(\chi_{8512}(69, \cdot)\) n/a 20416 16
8512.2.jj \(\chi_{8512}(197, \cdot)\) n/a 15360 16
8512.2.jw \(\chi_{8512}(277, \cdot)\) n/a 20416 16
8512.2.jx \(\chi_{8512}(677, \cdot)\) n/a 20416 16
8512.2.jy \(\chi_{8512}(467, \cdot)\) n/a 20416 16
8512.2.jz \(\chi_{8512}(115, \cdot)\) n/a 18432 16
8512.2.ka \(\chi_{8512}(331, \cdot)\) n/a 20416 16
8512.2.kb \(\chi_{8512}(683, \cdot)\) n/a 20416 16
8512.2.kc \(\chi_{8512}(837, \cdot)\) n/a 18432 16
8512.2.kd \(\chi_{8512}(429, \cdot)\) n/a 20416 16
8512.2.ke \(\chi_{8512}(341, \cdot)\) n/a 20416 16
8512.2.kf \(\chi_{8512}(829, \cdot)\) n/a 20416 16
8512.2.kg \(\chi_{8512}(619, \cdot)\) n/a 20416 16
8512.2.kh \(\chi_{8512}(107, \cdot)\) n/a 20416 16
8512.2.kq \(\chi_{8512}(25, \cdot)\) None 0 24
8512.2.kr \(\chi_{8512}(55, \cdot)\) None 0 24
8512.2.ks \(\chi_{8512}(169, \cdot)\) None 0 24
8512.2.kt \(\chi_{8512}(199, \cdot)\) None 0 24
8512.2.ku \(\chi_{8512}(409, \cdot)\) None 0 24
8512.2.kv \(\chi_{8512}(71, \cdot)\) None 0 24
8512.2.kw \(\chi_{8512}(41, \cdot)\) None 0 24
8512.2.kx \(\chi_{8512}(135, \cdot)\) None 0 24
8512.2.lg \(\chi_{8512}(375, \cdot)\) None 0 24
8512.2.lh \(\chi_{8512}(89, \cdot)\) None 0 24
8512.2.li \(\chi_{8512}(215, \cdot)\) None 0 24
8512.2.lj \(\chi_{8512}(9, \cdot)\) None 0 24
8512.2.lk \(\chi_{8512}(269, \cdot)\) n/a 61248 48
8512.2.ll \(\chi_{8512}(51, \cdot)\) n/a 61248 48
8512.2.lm \(\chi_{8512}(541, \cdot)\) n/a 61248 48
8512.2.ln \(\chi_{8512}(283, \cdot)\) n/a 61248 48
8512.2.lw \(\chi_{8512}(93, \cdot)\) n/a 61248 48
8512.2.lx \(\chi_{8512}(131, \cdot)\) n/a 61248 48
8512.2.ly \(\chi_{8512}(139, \cdot)\) n/a 61248 48
8512.2.lz \(\chi_{8512}(85, \cdot)\) n/a 46080 48
8512.2.ma \(\chi_{8512}(155, \cdot)\) n/a 46080 48
8512.2.mb \(\chi_{8512}(13, \cdot)\) n/a 61248 48
8512.2.mc \(\chi_{8512}(117, \cdot)\) n/a 61248 48
8512.2.md \(\chi_{8512}(67, \cdot)\) n/a 61248 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8512))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8512)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1064))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4256))\)\(^{\oplus 2}\)