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Properties

Label 6045.2
Level 6045
Weight 2
Dimension 870817
Nonzero newspaces 200
Sturm bound 5160960

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Defining parameters

Level: \( N \) = \( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 200 \)
Sturm bound: \(5160960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6045))\).

Total New Old
Modular forms 1301760 878481 423279
Cusp forms 1278721 870817 407904
Eisenstein series 23039 7664 15375

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6045))\)

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
6045.2.a \(\chi_{6045}(1, \cdot)\) 6045.2.a.a 1 1
6045.2.a.b 1
6045.2.a.c 1
6045.2.a.d 1
6045.2.a.e 1
6045.2.a.f 1
6045.2.a.g 1
6045.2.a.h 1
6045.2.a.i 1
6045.2.a.j 1
6045.2.a.k 1
6045.2.a.l 1
6045.2.a.m 2
6045.2.a.n 2
6045.2.a.o 2
6045.2.a.p 2
6045.2.a.q 3
6045.2.a.r 3
6045.2.a.s 5
6045.2.a.t 9
6045.2.a.u 9
6045.2.a.v 10
6045.2.a.w 11
6045.2.a.x 12
6045.2.a.y 12
6045.2.a.z 12
6045.2.a.ba 13
6045.2.a.bb 13
6045.2.a.bc 14
6045.2.a.bd 14
6045.2.a.be 15
6045.2.a.bf 15
6045.2.a.bg 16
6045.2.a.bh 17
6045.2.a.bi 18
6045.2.b \(\chi_{6045}(2326, \cdot)\) n/a 280 1
6045.2.e \(\chi_{6045}(2419, \cdot)\) n/a 360 1
6045.2.f \(\chi_{6045}(6044, \cdot)\) n/a 888 1
6045.2.i \(\chi_{6045}(1301, \cdot)\) n/a 512 1
6045.2.j \(\chi_{6045}(3626, \cdot)\) n/a 600 1
6045.2.m \(\chi_{6045}(3719, \cdot)\) n/a 768 1
6045.2.n \(\chi_{6045}(4744, \cdot)\) n/a 416 1
6045.2.q \(\chi_{6045}(3136, \cdot)\) n/a 596 2
6045.2.r \(\chi_{6045}(2791, \cdot)\) n/a 560 2
6045.2.s \(\chi_{6045}(211, \cdot)\) n/a 596 2
6045.2.t \(\chi_{6045}(2536, \cdot)\) n/a 512 2
6045.2.u \(\chi_{6045}(1487, \cdot)\) n/a 1776 2
6045.2.w \(\chi_{6045}(5023, \cdot)\) n/a 840 2
6045.2.y \(\chi_{6045}(898, \cdot)\) n/a 768 2
6045.2.ba \(\chi_{6045}(1613, \cdot)\) n/a 1440 2
6045.2.bc \(\chi_{6045}(1334, \cdot)\) n/a 1680 2
6045.2.be \(\chi_{6045}(4961, \cdot)\) n/a 1120 2
6045.2.bg \(\chi_{6045}(619, \cdot)\) n/a 896 2
6045.2.bi \(\chi_{6045}(4246, \cdot)\) n/a 592 2
6045.2.bl \(\chi_{6045}(3223, \cdot)\) n/a 896 2
6045.2.bn \(\chi_{6045}(3938, \cdot)\) n/a 1680 2
6045.2.bo \(\chi_{6045}(187, \cdot)\) n/a 840 2
6045.2.bq \(\chi_{6045}(278, \cdot)\) n/a 1776 2
6045.2.bs \(\chi_{6045}(1366, \cdot)\) n/a 1024 4
6045.2.bt \(\chi_{6045}(1886, \cdot)\) n/a 1024 2
6045.2.bw \(\chi_{6045}(584, \cdot)\) n/a 1776 2
6045.2.bx \(\chi_{6045}(1834, \cdot)\) n/a 768 2
6045.2.ca \(\chi_{6045}(1741, \cdot)\) n/a 600 2
6045.2.cb \(\chi_{6045}(1421, \cdot)\) n/a 1196 2
6045.2.ce \(\chi_{6045}(1049, \cdot)\) n/a 1776 2
6045.2.ci \(\chi_{6045}(439, \cdot)\) n/a 896 2
6045.2.ck \(\chi_{6045}(1024, \cdot)\) n/a 832 2
6045.2.cl \(\chi_{6045}(464, \cdot)\) n/a 1776 2
6045.2.cn \(\chi_{6045}(1979, \cdot)\) n/a 1776 2
6045.2.cq \(\chi_{6045}(836, \cdot)\) n/a 1192 2
6045.2.cs \(\chi_{6045}(491, \cdot)\) n/a 1196 2
6045.2.ct \(\chi_{6045}(1369, \cdot)\) n/a 896 2
6045.2.cw \(\chi_{6045}(1141, \cdot)\) n/a 596 2
6045.2.cz \(\chi_{6045}(2629, \cdot)\) n/a 896 2
6045.2.da \(\chi_{6045}(4091, \cdot)\) n/a 1192 2
6045.2.dc \(\chi_{6045}(1556, \cdot)\) n/a 1196 2
6045.2.df \(\chi_{6045}(2324, \cdot)\) n/a 1776 2
6045.2.dh \(\chi_{6045}(719, \cdot)\) n/a 1776 2
6045.2.di \(\chi_{6045}(1699, \cdot)\) n/a 896 2
6045.2.dk \(\chi_{6045}(94, \cdot)\) n/a 848 2
6045.2.dn \(\chi_{6045}(2071, \cdot)\) n/a 596 2
6045.2.dp \(\chi_{6045}(4651, \cdot)\) n/a 560 2
6045.2.dq \(\chi_{6045}(3839, \cdot)\) n/a 1776 2
6045.2.dt \(\chi_{6045}(2486, \cdot)\) n/a 1196 2
6045.2.dw \(\chi_{6045}(1234, \cdot)\) n/a 896 2
6045.2.dx \(\chi_{6045}(1184, \cdot)\) n/a 1536 2
6045.2.ea \(\chi_{6045}(1091, \cdot)\) n/a 1192 2
6045.2.ed \(\chi_{6045}(64, \cdot)\) n/a 1792 4
6045.2.ee \(\chi_{6045}(209, \cdot)\) n/a 3072 4
6045.2.eh \(\chi_{6045}(116, \cdot)\) n/a 2400 4
6045.2.ei \(\chi_{6045}(3251, \cdot)\) n/a 2048 4
6045.2.el \(\chi_{6045}(1949, \cdot)\) n/a 3552 4
6045.2.em \(\chi_{6045}(469, \cdot)\) n/a 1536 4
6045.2.ep \(\chi_{6045}(376, \cdot)\) n/a 1184 4
6045.2.eq \(\chi_{6045}(1513, \cdot)\) n/a 1792 4
6045.2.es \(\chi_{6045}(398, \cdot)\) n/a 3552 4
6045.2.ev \(\chi_{6045}(583, \cdot)\) n/a 1792 4
6045.2.ex \(\chi_{6045}(1142, \cdot)\) n/a 3552 4
6045.2.ez \(\chi_{6045}(557, \cdot)\) n/a 3552 4
6045.2.fb \(\chi_{6045}(652, \cdot)\) n/a 1680 4
6045.2.fd \(\chi_{6045}(67, \cdot)\) n/a 1792 4
6045.2.ff \(\chi_{6045}(2723, \cdot)\) n/a 3552 4
6045.2.fg \(\chi_{6045}(428, \cdot)\) n/a 3552 4
6045.2.fi \(\chi_{6045}(688, \cdot)\) n/a 1792 4
6045.2.fk \(\chi_{6045}(1711, \cdot)\) n/a 1200 4
6045.2.fm \(\chi_{6045}(1204, \cdot)\) n/a 1792 4
6045.2.fo \(\chi_{6045}(1451, \cdot)\) n/a 2384 4
6045.2.fq \(\chi_{6045}(749, \cdot)\) n/a 3552 4
6045.2.ft \(\chi_{6045}(1028, \cdot)\) n/a 3072 4
6045.2.fv \(\chi_{6045}(1483, \cdot)\) n/a 1536 4
6045.2.fw \(\chi_{6045}(1823, \cdot)\) n/a 3552 4
6045.2.fy \(\chi_{6045}(2083, \cdot)\) n/a 1792 4
6045.2.ga \(\chi_{6045}(433, \cdot)\) n/a 1792 4
6045.2.gc \(\chi_{6045}(842, \cdot)\) n/a 3552 4
6045.2.ge \(\chi_{6045}(88, \cdot)\) n/a 1792 4
6045.2.gg \(\chi_{6045}(218, \cdot)\) n/a 3360 4
6045.2.gj \(\chi_{6045}(1241, \cdot)\) n/a 2240 4
6045.2.gl \(\chi_{6045}(869, \cdot)\) n/a 3360 4
6045.2.gn \(\chi_{6045}(3529, \cdot)\) n/a 1792 4
6045.2.gp \(\chi_{6045}(4036, \cdot)\) n/a 1192 4
6045.2.gr \(\chi_{6045}(409, \cdot)\) n/a 1792 4
6045.2.gt \(\chi_{6045}(1111, \cdot)\) n/a 1192 4
6045.2.gv \(\chi_{6045}(3074, \cdot)\) n/a 3552 4
6045.2.gx \(\chi_{6045}(3776, \cdot)\) n/a 2392 4
6045.2.gz \(\chi_{6045}(149, \cdot)\) n/a 3552 4
6045.2.hb \(\chi_{6045}(656, \cdot)\) n/a 2392 4
6045.2.hd \(\chi_{6045}(526, \cdot)\) n/a 1200 4
6045.2.hf \(\chi_{6045}(154, \cdot)\) n/a 1792 4
6045.2.hh \(\chi_{6045}(3688, \cdot)\) n/a 1792 4
6045.2.hj \(\chi_{6045}(893, \cdot)\) n/a 3552 4
6045.2.hl \(\chi_{6045}(367, \cdot)\) n/a 1792 4
6045.2.hn \(\chi_{6045}(497, \cdot)\) n/a 3360 4
6045.2.hp \(\chi_{6045}(563, \cdot)\) n/a 3552 4
6045.2.hr \(\chi_{6045}(1018, \cdot)\) n/a 1792 4
6045.2.ht \(\chi_{6045}(2858, \cdot)\) n/a 3552 4
6045.2.hv \(\chi_{6045}(838, \cdot)\) n/a 1680 4
6045.2.hx \(\chi_{6045}(397, \cdot)\) n/a 1792 4
6045.2.hz \(\chi_{6045}(812, \cdot)\) n/a 3552 4
6045.2.ib \(\chi_{6045}(1952, \cdot)\) n/a 3552 4
6045.2.id \(\chi_{6045}(253, \cdot)\) n/a 1792 4
6045.2.ie \(\chi_{6045}(863, \cdot)\) n/a 3552 4
6045.2.ig \(\chi_{6045}(1048, \cdot)\) n/a 1792 4
6045.2.ii \(\chi_{6045}(196, \cdot)\) n/a 2048 8
6045.2.ij \(\chi_{6045}(1621, \cdot)\) n/a 2384 8
6045.2.ik \(\chi_{6045}(16, \cdot)\) n/a 2400 8
6045.2.il \(\chi_{6045}(2401, \cdot)\) n/a 2384 8
6045.2.in \(\chi_{6045}(2228, \cdot)\) n/a 7104 8
6045.2.ip \(\chi_{6045}(853, \cdot)\) n/a 3584 8
6045.2.iq \(\chi_{6045}(233, \cdot)\) n/a 7104 8
6045.2.is \(\chi_{6045}(337, \cdot)\) n/a 3584 8
6045.2.iv \(\chi_{6045}(151, \cdot)\) n/a 2368 8
6045.2.ix \(\chi_{6045}(2569, \cdot)\) n/a 3584 8
6045.2.iz \(\chi_{6045}(281, \cdot)\) n/a 4800 8
6045.2.jb \(\chi_{6045}(2699, \cdot)\) n/a 7104 8
6045.2.jd \(\chi_{6045}(287, \cdot)\) n/a 6144 8
6045.2.jf \(\chi_{6045}(742, \cdot)\) n/a 3072 8
6045.2.jh \(\chi_{6045}(343, \cdot)\) n/a 3584 8
6045.2.jj \(\chi_{6045}(122, \cdot)\) n/a 7104 8
6045.2.jk \(\chi_{6045}(1481, \cdot)\) n/a 4768 8
6045.2.jn \(\chi_{6045}(1574, \cdot)\) n/a 6144 8
6045.2.jo \(\chi_{6045}(454, \cdot)\) n/a 3584 8
6045.2.jr \(\chi_{6045}(2336, \cdot)\) n/a 4784 8
6045.2.ju \(\chi_{6045}(179, \cdot)\) n/a 7104 8
6045.2.jv \(\chi_{6045}(901, \cdot)\) n/a 2400 8
6045.2.jx \(\chi_{6045}(121, \cdot)\) n/a 2384 8
6045.2.ka \(\chi_{6045}(529, \cdot)\) n/a 3584 8
6045.2.kc \(\chi_{6045}(289, \cdot)\) n/a 3584 8
6045.2.kd \(\chi_{6045}(569, \cdot)\) n/a 7104 8
6045.2.kf \(\chi_{6045}(914, \cdot)\) n/a 7104 8
6045.2.ki \(\chi_{6045}(146, \cdot)\) n/a 4784 8
6045.2.kk \(\chi_{6045}(581, \cdot)\) n/a 4768 8
6045.2.kl \(\chi_{6045}(484, \cdot)\) n/a 3584 8
6045.2.ko \(\chi_{6045}(751, \cdot)\) n/a 2384 8
6045.2.kr \(\chi_{6045}(634, \cdot)\) n/a 3584 8
6045.2.ks \(\chi_{6045}(251, \cdot)\) n/a 4784 8
6045.2.ku \(\chi_{6045}(1856, \cdot)\) n/a 4768 8
6045.2.kx \(\chi_{6045}(74, \cdot)\) n/a 7104 8
6045.2.kz \(\chi_{6045}(29, \cdot)\) n/a 7104 8
6045.2.la \(\chi_{6045}(4, \cdot)\) n/a 3584 8
6045.2.lc \(\chi_{6045}(49, \cdot)\) n/a 3584 8
6045.2.lg \(\chi_{6045}(269, \cdot)\) n/a 7104 8
6045.2.lj \(\chi_{6045}(296, \cdot)\) n/a 4784 8
6045.2.lk \(\chi_{6045}(1156, \cdot)\) n/a 2400 8
6045.2.ln \(\chi_{6045}(1249, \cdot)\) n/a 3072 8
6045.2.lo \(\chi_{6045}(389, \cdot)\) n/a 7104 8
6045.2.lr \(\chi_{6045}(716, \cdot)\) n/a 4096 8
6045.2.lt \(\chi_{6045}(268, \cdot)\) n/a 7168 16
6045.2.lv \(\chi_{6045}(83, \cdot)\) n/a 14208 16
6045.2.lw \(\chi_{6045}(28, \cdot)\) n/a 7168 16
6045.2.ly \(\chi_{6045}(488, \cdot)\) n/a 14208 16
6045.2.ma \(\chi_{6045}(197, \cdot)\) n/a 14208 16
6045.2.mc \(\chi_{6045}(7, \cdot)\) n/a 7168 16
6045.2.me \(\chi_{6045}(202, \cdot)\) n/a 7168 16
6045.2.mg \(\chi_{6045}(1367, \cdot)\) n/a 14208 16
6045.2.mi \(\chi_{6045}(127, \cdot)\) n/a 7168 16
6045.2.mk \(\chi_{6045}(173, \cdot)\) n/a 14208 16
6045.2.mm \(\chi_{6045}(653, \cdot)\) n/a 14208 16
6045.2.mo \(\chi_{6045}(757, \cdot)\) n/a 7168 16
6045.2.mq \(\chi_{6045}(152, \cdot)\) n/a 14208 16
6045.2.ms \(\chi_{6045}(178, \cdot)\) n/a 7168 16
6045.2.mu \(\chi_{6045}(184, \cdot)\) n/a 7168 16
6045.2.mw \(\chi_{6045}(46, \cdot)\) n/a 4800 16
6045.2.my \(\chi_{6045}(71, \cdot)\) n/a 9568 16
6045.2.na \(\chi_{6045}(59, \cdot)\) n/a 14208 16
6045.2.nc \(\chi_{6045}(41, \cdot)\) n/a 9568 16
6045.2.ne \(\chi_{6045}(479, \cdot)\) n/a 14208 16
6045.2.ng \(\chi_{6045}(331, \cdot)\) n/a 4768 16
6045.2.ni \(\chi_{6045}(799, \cdot)\) n/a 7168 16
6045.2.nk \(\chi_{6045}(106, \cdot)\) n/a 4768 16
6045.2.nm \(\chi_{6045}(544, \cdot)\) n/a 7168 16
6045.2.no \(\chi_{6045}(314, \cdot)\) n/a 14208 16
6045.2.nq \(\chi_{6045}(566, \cdot)\) n/a 9536 16
6045.2.nt \(\chi_{6045}(407, \cdot)\) n/a 14208 16
6045.2.nv \(\chi_{6045}(43, \cdot)\) n/a 7168 16
6045.2.nx \(\chi_{6045}(257, \cdot)\) n/a 14208 16
6045.2.nz \(\chi_{6045}(277, \cdot)\) n/a 7168 16
6045.2.ob \(\chi_{6045}(22, \cdot)\) n/a 7168 16
6045.2.od \(\chi_{6045}(107, \cdot)\) n/a 14208 16
6045.2.oe \(\chi_{6045}(313, \cdot)\) n/a 6144 16
6045.2.og \(\chi_{6045}(443, \cdot)\) n/a 12288 16
6045.2.oj \(\chi_{6045}(164, \cdot)\) n/a 14208 16
6045.2.ol \(\chi_{6045}(671, \cdot)\) n/a 9536 16
6045.2.on \(\chi_{6045}(34, \cdot)\) n/a 7168 16
6045.2.op \(\chi_{6045}(2101, \cdot)\) n/a 4800 16
6045.2.or \(\chi_{6045}(1078, \cdot)\) n/a 7168 16
6045.2.ot \(\chi_{6045}(38, \cdot)\) n/a 14208 16
6045.2.ou \(\chi_{6045}(137, \cdot)\) n/a 14208 16
6045.2.ow \(\chi_{6045}(847, \cdot)\) n/a 7168 16
6045.2.oy \(\chi_{6045}(97, \cdot)\) n/a 7168 16
6045.2.pa \(\chi_{6045}(773, \cdot)\) n/a 14208 16
6045.2.pc \(\chi_{6045}(362, \cdot)\) n/a 14208 16
6045.2.pe \(\chi_{6045}(193, \cdot)\) n/a 7168 16
6045.2.ph \(\chi_{6045}(203, \cdot)\) n/a 14208 16
6045.2.pj \(\chi_{6045}(112, \cdot)\) n/a 7168 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6045))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6045)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(403))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1209))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2015))\)\(^{\oplus 2}\)