Properties

Label 8001.2
Level 8001
Weight 2
Dimension 1756140
Nonzero newspaces 184
Sturm bound 9289728

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Defining parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 184 \)
Sturm bound: \(9289728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8001))\).

Total New Old
Modular forms 2334528 1767392 567136
Cusp forms 2310337 1756140 554197
Eisenstein series 24191 11252 12939

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8001))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
8001.2.a \(\chi_{8001}(1, \cdot)\) 8001.2.a.a 1 1
8001.2.a.b 1
8001.2.a.c 1
8001.2.a.d 1
8001.2.a.e 1
8001.2.a.f 1
8001.2.a.g 1
8001.2.a.h 2
8001.2.a.i 2
8001.2.a.j 2
8001.2.a.k 2
8001.2.a.l 7
8001.2.a.m 11
8001.2.a.n 12
8001.2.a.o 13
8001.2.a.p 14
8001.2.a.q 15
8001.2.a.r 16
8001.2.a.s 16
8001.2.a.t 16
8001.2.a.u 18
8001.2.a.v 19
8001.2.a.w 20
8001.2.a.x 22
8001.2.a.y 28
8001.2.a.z 32
8001.2.a.ba 40
8001.2.d \(\chi_{8001}(7748, \cdot)\) n/a 336 1
8001.2.e \(\chi_{8001}(1142, \cdot)\) n/a 256 1
8001.2.h \(\chi_{8001}(7111, \cdot)\) n/a 426 1
8001.2.i \(\chi_{8001}(361, \cdot)\) n/a 848 2
8001.2.j \(\chi_{8001}(4573, \cdot)\) n/a 840 2
8001.2.k \(\chi_{8001}(3448, \cdot)\) n/a 848 2
8001.2.l \(\chi_{8001}(400, \cdot)\) n/a 1536 2
8001.2.m \(\chi_{8001}(2668, \cdot)\) n/a 1512 2
8001.2.n \(\chi_{8001}(3067, \cdot)\) n/a 1536 2
8001.2.o \(\chi_{8001}(4552, \cdot)\) n/a 2040 2
8001.2.p \(\chi_{8001}(3028, \cdot)\) n/a 2040 2
8001.2.q \(\chi_{8001}(382, \cdot)\) n/a 2016 2
8001.2.r \(\chi_{8001}(3049, \cdot)\) n/a 2016 2
8001.2.s \(\chi_{8001}(781, \cdot)\) n/a 2040 2
8001.2.t \(\chi_{8001}(4972, \cdot)\) n/a 2040 2
8001.2.u \(\chi_{8001}(2647, \cdot)\) n/a 640 2
8001.2.x \(\chi_{8001}(5315, \cdot)\) n/a 2040 2
8001.2.y \(\chi_{8001}(6242, \cdot)\) n/a 2040 2
8001.2.z \(\chi_{8001}(2432, \cdot)\) n/a 2040 2
8001.2.ba \(\chi_{8001}(1523, \cdot)\) n/a 2040 2
8001.2.bb \(\chi_{8001}(509, \cdot)\) n/a 2016 2
8001.2.bc \(\chi_{8001}(401, \cdot)\) n/a 2040 2
8001.2.bj \(\chi_{8001}(3410, \cdot)\) n/a 512 2
8001.2.bk \(\chi_{8001}(2393, \cdot)\) n/a 688 2
8001.2.br \(\chi_{8001}(1396, \cdot)\) n/a 848 2
8001.2.bs \(\chi_{8001}(4807, \cdot)\) n/a 848 2
8001.2.bt \(\chi_{8001}(3664, \cdot)\) n/a 848 2
8001.2.bu \(\chi_{8001}(1777, \cdot)\) n/a 2040 2
8001.2.bv \(\chi_{8001}(1798, \cdot)\) n/a 2040 2
8001.2.bw \(\chi_{8001}(6712, \cdot)\) n/a 2040 2
8001.2.cj \(\chi_{8001}(1417, \cdot)\) n/a 2040 2
8001.2.ck \(\chi_{8001}(5227, \cdot)\) n/a 2040 2
8001.2.cl \(\chi_{8001}(4063, \cdot)\) n/a 2040 2
8001.2.cs \(\chi_{8001}(146, \cdot)\) n/a 2040 2
8001.2.ct \(\chi_{8001}(3830, \cdot)\) n/a 1536 2
8001.2.cu \(\chi_{8001}(3809, \cdot)\) n/a 1536 2
8001.2.cv \(\chi_{8001}(743, \cdot)\) n/a 1536 2
8001.2.cw \(\chi_{8001}(2813, \cdot)\) n/a 2040 2
8001.2.cx \(\chi_{8001}(2414, \cdot)\) n/a 2016 2
8001.2.cy \(\chi_{8001}(1124, \cdot)\) n/a 680 2
8001.2.cz \(\chi_{8001}(5822, \cdot)\) n/a 680 2
8001.2.da \(\chi_{8001}(2033, \cdot)\) n/a 672 2
8001.2.db \(\chi_{8001}(4211, \cdot)\) n/a 680 2
8001.2.dc \(\chi_{8001}(908, \cdot)\) n/a 680 2
8001.2.dd \(\chi_{8001}(5714, \cdot)\) n/a 680 2
8001.2.dq \(\chi_{8001}(380, \cdot)\) n/a 2040 2
8001.2.dr \(\chi_{8001}(5843, \cdot)\) n/a 2016 2
8001.2.ds \(\chi_{8001}(2012, \cdot)\) n/a 2040 2
8001.2.dt \(\chi_{8001}(5735, \cdot)\) n/a 2040 2
8001.2.du \(\chi_{8001}(488, \cdot)\) n/a 2040 2
8001.2.dv \(\chi_{8001}(1544, \cdot)\) n/a 2040 2
8001.2.dy \(\chi_{8001}(997, \cdot)\) n/a 2040 2
8001.2.dz \(\chi_{8001}(5206, \cdot)\) n/a 2040 2
8001.2.ea \(\chi_{8001}(4084, \cdot)\) n/a 2040 2
8001.2.eh \(\chi_{8001}(1378, \cdot)\) n/a 852 2
8001.2.ei \(\chi_{8001}(64, \cdot)\) n/a 1920 6
8001.2.ej \(\chi_{8001}(3481, \cdot)\) n/a 6120 6
8001.2.ek \(\chi_{8001}(22, \cdot)\) n/a 4608 6
8001.2.el \(\chi_{8001}(37, \cdot)\) n/a 2550 6
8001.2.em \(\chi_{8001}(1465, \cdot)\) n/a 6120 6
8001.2.en \(\chi_{8001}(799, \cdot)\) n/a 4608 6
8001.2.eo \(\chi_{8001}(226, \cdot)\) n/a 2550 6
8001.2.ep \(\chi_{8001}(1576, \cdot)\) n/a 1920 6
8001.2.eq \(\chi_{8001}(403, \cdot)\) n/a 6120 6
8001.2.er \(\chi_{8001}(2704, \cdot)\) n/a 6120 6
8001.2.es \(\chi_{8001}(1000, \cdot)\) n/a 2556 6
8001.2.ev \(\chi_{8001}(1079, \cdot)\) n/a 1536 6
8001.2.ew \(\chi_{8001}(3842, \cdot)\) n/a 2064 6
8001.2.fb \(\chi_{8001}(1583, \cdot)\) n/a 1536 6
8001.2.fc \(\chi_{8001}(1472, \cdot)\) n/a 6120 6
8001.2.fd \(\chi_{8001}(164, \cdot)\) n/a 6120 6
8001.2.fe \(\chi_{8001}(1322, \cdot)\) n/a 2040 6
8001.2.fj \(\chi_{8001}(68, \cdot)\) n/a 6120 6
8001.2.fk \(\chi_{8001}(3488, \cdot)\) n/a 6120 6
8001.2.fp \(\chi_{8001}(790, \cdot)\) n/a 6120 6
8001.2.fq \(\chi_{8001}(598, \cdot)\) n/a 6120 6
8001.2.fr \(\chi_{8001}(313, \cdot)\) n/a 6120 6
8001.2.fs \(\chi_{8001}(2980, \cdot)\) n/a 2550 6
8001.2.gb \(\chi_{8001}(964, \cdot)\) n/a 2550 6
8001.2.gc \(\chi_{8001}(202, \cdot)\) n/a 6120 6
8001.2.gh \(\chi_{8001}(530, \cdot)\) n/a 2052 6
8001.2.gi \(\chi_{8001}(941, \cdot)\) n/a 6120 6
8001.2.gj \(\chi_{8001}(536, \cdot)\) n/a 6120 6
8001.2.gk \(\chi_{8001}(359, \cdot)\) n/a 2052 6
8001.2.gl \(\chi_{8001}(155, \cdot)\) n/a 4608 6
8001.2.gm \(\chi_{8001}(725, \cdot)\) n/a 6120 6
8001.2.gn \(\chi_{8001}(992, \cdot)\) n/a 6120 6
8001.2.go \(\chi_{8001}(545, \cdot)\) n/a 6120 6
8001.2.gx \(\chi_{8001}(1502, \cdot)\) n/a 2052 6
8001.2.gy \(\chi_{8001}(344, \cdot)\) n/a 4608 6
8001.2.gz \(\chi_{8001}(230, \cdot)\) n/a 6120 6
8001.2.ha \(\chi_{8001}(1592, \cdot)\) n/a 2052 6
8001.2.hd \(\chi_{8001}(1375, \cdot)\) n/a 6120 6
8001.2.he \(\chi_{8001}(1756, \cdot)\) n/a 2544 6
8001.2.hj \(\chi_{8001}(1741, \cdot)\) n/a 6120 6
8001.2.hk \(\chi_{8001}(442, \cdot)\) n/a 3840 12
8001.2.hl \(\chi_{8001}(214, \cdot)\) n/a 12240 12
8001.2.hm \(\chi_{8001}(25, \cdot)\) n/a 12240 12
8001.2.hn \(\chi_{8001}(1159, \cdot)\) n/a 12240 12
8001.2.ho \(\chi_{8001}(4, \cdot)\) n/a 12240 12
8001.2.hp \(\chi_{8001}(457, \cdot)\) n/a 12240 12
8001.2.hq \(\chi_{8001}(2209, \cdot)\) n/a 12240 12
8001.2.hr \(\chi_{8001}(673, \cdot)\) n/a 9216 12
8001.2.hs \(\chi_{8001}(778, \cdot)\) n/a 9216 12
8001.2.ht \(\chi_{8001}(1219, \cdot)\) n/a 9216 12
8001.2.hu \(\chi_{8001}(856, \cdot)\) n/a 5088 12
8001.2.hv \(\chi_{8001}(667, \cdot)\) n/a 5088 12
8001.2.hw \(\chi_{8001}(100, \cdot)\) n/a 5088 12
8001.2.hx \(\chi_{8001}(181, \cdot)\) n/a 5112 12
8001.2.ie \(\chi_{8001}(229, \cdot)\) n/a 12240 12
8001.2.if \(\chi_{8001}(619, \cdot)\) n/a 12240 12
8001.2.ig \(\chi_{8001}(40, \cdot)\) n/a 12240 12
8001.2.ij \(\chi_{8001}(1451, \cdot)\) n/a 12240 12
8001.2.ik \(\chi_{8001}(47, \cdot)\) n/a 12240 12
8001.2.il \(\chi_{8001}(662, \cdot)\) n/a 12240 12
8001.2.im \(\chi_{8001}(122, \cdot)\) n/a 12240 12
8001.2.in \(\chi_{8001}(1937, \cdot)\) n/a 12240 12
8001.2.io \(\chi_{8001}(95, \cdot)\) n/a 12240 12
8001.2.jb \(\chi_{8001}(746, \cdot)\) n/a 4080 12
8001.2.jc \(\chi_{8001}(152, \cdot)\) n/a 4080 12
8001.2.jd \(\chi_{8001}(737, \cdot)\) n/a 4080 12
8001.2.je \(\chi_{8001}(143, \cdot)\) n/a 4080 12
8001.2.jf \(\chi_{8001}(341, \cdot)\) n/a 4080 12
8001.2.jg \(\chi_{8001}(305, \cdot)\) n/a 4080 12
8001.2.jh \(\chi_{8001}(524, \cdot)\) n/a 12240 12
8001.2.ji \(\chi_{8001}(419, \cdot)\) n/a 12240 12
8001.2.jj \(\chi_{8001}(1499, \cdot)\) n/a 9216 12
8001.2.jk \(\chi_{8001}(365, \cdot)\) n/a 9216 12
8001.2.jl \(\chi_{8001}(281, \cdot)\) n/a 9216 12
8001.2.jm \(\chi_{8001}(965, \cdot)\) n/a 12240 12
8001.2.jt \(\chi_{8001}(250, \cdot)\) n/a 12240 12
8001.2.ju \(\chi_{8001}(535, \cdot)\) n/a 12240 12
8001.2.jv \(\chi_{8001}(943, \cdot)\) n/a 12240 12
8001.2.ki \(\chi_{8001}(391, \cdot)\) n/a 12240 12
8001.2.kj \(\chi_{8001}(160, \cdot)\) n/a 12240 12
8001.2.kk \(\chi_{8001}(349, \cdot)\) n/a 12240 12
8001.2.kl \(\chi_{8001}(334, \cdot)\) n/a 5088 12
8001.2.km \(\chi_{8001}(10, \cdot)\) n/a 5088 12
8001.2.kn \(\chi_{8001}(1333, \cdot)\) n/a 5088 12
8001.2.ku \(\chi_{8001}(188, \cdot)\) n/a 4128 12
8001.2.kv \(\chi_{8001}(386, \cdot)\) n/a 3072 12
8001.2.lc \(\chi_{8001}(842, \cdot)\) n/a 12240 12
8001.2.ld \(\chi_{8001}(131, \cdot)\) n/a 12240 12
8001.2.le \(\chi_{8001}(1460, \cdot)\) n/a 12240 12
8001.2.lf \(\chi_{8001}(38, \cdot)\) n/a 12240 12
8001.2.lg \(\chi_{8001}(983, \cdot)\) n/a 12240 12
8001.2.lh \(\chi_{8001}(137, \cdot)\) n/a 12240 12
8001.2.lk \(\chi_{8001}(970, \cdot)\) n/a 36720 36
8001.2.ll \(\chi_{8001}(88, \cdot)\) n/a 36720 36
8001.2.lm \(\chi_{8001}(316, \cdot)\) n/a 11520 36
8001.2.ln \(\chi_{8001}(289, \cdot)\) n/a 15300 36
8001.2.lo \(\chi_{8001}(169, \cdot)\) n/a 27648 36
8001.2.lp \(\chi_{8001}(646, \cdot)\) n/a 36720 36
8001.2.lq \(\chi_{8001}(163, \cdot)\) n/a 15300 36
8001.2.lr \(\chi_{8001}(148, \cdot)\) n/a 27648 36
8001.2.ls \(\chi_{8001}(79, \cdot)\) n/a 36720 36
8001.2.lt \(\chi_{8001}(166, \cdot)\) n/a 36720 36
8001.2.ly \(\chi_{8001}(55, \cdot)\) n/a 15264 36
8001.2.lz \(\chi_{8001}(355, \cdot)\) n/a 36720 36
8001.2.mc \(\chi_{8001}(29, \cdot)\) n/a 27648 36
8001.2.md \(\chi_{8001}(53, \cdot)\) n/a 12312 36
8001.2.me \(\chi_{8001}(17, \cdot)\) n/a 12312 36
8001.2.mf \(\chi_{8001}(104, \cdot)\) n/a 36720 36
8001.2.mo \(\chi_{8001}(65, \cdot)\) n/a 36720 36
8001.2.mp \(\chi_{8001}(92, \cdot)\) n/a 27648 36
8001.2.mq \(\chi_{8001}(41, \cdot)\) n/a 36720 36
8001.2.mr \(\chi_{8001}(866, \cdot)\) n/a 36720 36
8001.2.ms \(\chi_{8001}(248, \cdot)\) n/a 36720 36
8001.2.mt \(\chi_{8001}(206, \cdot)\) n/a 12312 36
8001.2.mu \(\chi_{8001}(170, \cdot)\) n/a 12312 36
8001.2.mv \(\chi_{8001}(473, \cdot)\) n/a 36720 36
8001.2.na \(\chi_{8001}(139, \cdot)\) n/a 36720 36
8001.2.nb \(\chi_{8001}(649, \cdot)\) n/a 15300 36
8001.2.nk \(\chi_{8001}(388, \cdot)\) n/a 15300 36
8001.2.nl \(\chi_{8001}(346, \cdot)\) n/a 36720 36
8001.2.nm \(\chi_{8001}(220, \cdot)\) n/a 36720 36
8001.2.nn \(\chi_{8001}(97, \cdot)\) n/a 36720 36
8001.2.ns \(\chi_{8001}(416, \cdot)\) n/a 36720 36
8001.2.nt \(\chi_{8001}(86, \cdot)\) n/a 36720 36
8001.2.ny \(\chi_{8001}(23, \cdot)\) n/a 36720 36
8001.2.nz \(\chi_{8001}(134, \cdot)\) n/a 9216 36
8001.2.oa \(\chi_{8001}(62, \cdot)\) n/a 12240 36
8001.2.ob \(\chi_{8001}(290, \cdot)\) n/a 36720 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8001))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8001)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(127))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(381))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(889))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1143))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2667))\)\(^{\oplus 2}\)