# Properties

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

## 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

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