# Properties

 Label 8023.2 Level 8023 Weight 2 Dimension 2.67214e+06 Nonzero newspaces 90 Sturm bound 1.07251e+07

# Learn more about

## Defining parameters

 Level: $$N$$ = $$8023 = 71 \cdot 113$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$90$$ Sturm bound: $$10725120$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8023))$$.

Total New Old
Modular forms 2689120 2687455 1665
Cusp forms 2673441 2672135 1306
Eisenstein series 15679 15320 359

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8023))$$

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
8023.2.a $$\chi_{8023}(1, \cdot)$$ 8023.2.a.a 3 1
8023.2.a.b 155
8023.2.a.c 158
8023.2.a.d 165
8023.2.a.e 172
8023.2.c $$\chi_{8023}(4971, \cdot)$$ n/a 666 1
8023.2.f $$\chi_{8023}(5326, \cdot)$$ n/a 1332 2
8023.2.g $$\chi_{8023}(1922, \cdot)$$ n/a 2688 4
8023.2.h $$\chi_{8023}(332, \cdot)$$ n/a 4092 6
8023.2.i $$\chi_{8023}(143, \cdot)$$ n/a 3996 6
8023.2.j $$\chi_{8023}(30, \cdot)$$ n/a 4092 6
8023.2.k $$\chi_{8023}(671, \cdot)$$ n/a 4092 6
8023.2.l $$\chi_{8023}(897, \cdot)$$ n/a 4092 6
8023.2.m $$\chi_{8023}(1244, \cdot)$$ n/a 4032 6
8023.2.n $$\chi_{8023}(162, \cdot)$$ n/a 4092 6
8023.2.o $$\chi_{8023}(1386, \cdot)$$ n/a 4092 6
8023.2.q $$\chi_{8023}(5468, \cdot)$$ n/a 2656 4
8023.2.s $$\chi_{8023}(338, \cdot)$$ n/a 2728 4
8023.2.u $$\chi_{8023}(456, \cdot)$$ n/a 4092 6
8023.2.bc $$\chi_{8023}(1468, \cdot)$$ n/a 4092 6
8023.2.be $$\chi_{8023}(1326, \cdot)$$ n/a 4092 6
8023.2.bh $$\chi_{8023}(742, \cdot)$$ n/a 4092 6
8023.2.bi $$\chi_{8023}(569, \cdot)$$ n/a 3996 6
8023.2.bj $$\chi_{8023}(233, \cdot)$$ n/a 4092 6
8023.2.bn $$\chi_{8023}(1227, \cdot)$$ n/a 4092 6
8023.2.bq $$\chi_{8023}(403, \cdot)$$ n/a 4092 6
8023.2.bt $$\chi_{8023}(638, \cdot)$$ n/a 5456 8
8023.2.bu $$\chi_{8023}(128, \cdot)$$ n/a 5456 8
8023.2.bx $$\chi_{8023}(258, \cdot)$$ n/a 8184 12
8023.2.by $$\chi_{8023}(2020, \cdot)$$ n/a 8184 12
8023.2.bz $$\chi_{8023}(872, \cdot)$$ n/a 8184 12
8023.2.ca $$\chi_{8023}(1031, \cdot)$$ n/a 8184 12
8023.2.cb $$\chi_{8023}(1776, \cdot)$$ n/a 7992 12
8023.2.cc $$\chi_{8023}(889, \cdot)$$ n/a 8184 12
8023.2.cj $$\chi_{8023}(392, \cdot)$$ n/a 8184 12
8023.2.ck $$\chi_{8023}(32, \cdot)$$ n/a 8184 12
8023.2.cm $$\chi_{8023}(16, \cdot)$$ n/a 16368 24
8023.2.cn $$\chi_{8023}(367, \cdot)$$ n/a 16368 24
8023.2.co $$\chi_{8023}(114, \cdot)$$ n/a 16128 24
8023.2.cp $$\chi_{8023}(129, \cdot)$$ n/a 16368 24
8023.2.cq $$\chi_{8023}(242, \cdot)$$ n/a 16368 24
8023.2.cr $$\chi_{8023}(109, \cdot)$$ n/a 16368 24
8023.2.cs $$\chi_{8023}(480, \cdot)$$ n/a 16368 24
8023.2.ct $$\chi_{8023}(49, \cdot)$$ n/a 16368 24
8023.2.cu $$\chi_{8023}(270, \cdot)$$ n/a 10912 16
8023.2.cw $$\chi_{8023}(174, \cdot)$$ n/a 16368 24
8023.2.cz $$\chi_{8023}(321, \cdot)$$ n/a 16368 24
8023.2.da $$\chi_{8023}(72, \cdot)$$ n/a 15936 24
8023.2.db $$\chi_{8023}(190, \cdot)$$ n/a 16368 24
8023.2.dc $$\chi_{8023}(314, \cdot)$$ n/a 16368 24
8023.2.dd $$\chi_{8023}(375, \cdot)$$ n/a 16368 24
8023.2.de $$\chi_{8023}(91, \cdot)$$ n/a 16368 24
8023.2.dl $$\chi_{8023}(669, \cdot)$$ n/a 16368 24
8023.2.dn $$\chi_{8023}(4, \cdot)$$ n/a 16368 24
8023.2.dq $$\chi_{8023}(83, \cdot)$$ n/a 16368 24
8023.2.du $$\chi_{8023}(572, \cdot)$$ n/a 16368 24
8023.2.dv $$\chi_{8023}(196, \cdot)$$ n/a 16368 24
8023.2.dw $$\chi_{8023}(436, \cdot)$$ n/a 16368 24
8023.2.dz $$\chi_{8023}(535, \cdot)$$ n/a 16368 24
8023.2.eb $$\chi_{8023}(225, \cdot)$$ n/a 16368 24
8023.2.ej $$\chi_{8023}(855, \cdot)$$ n/a 16368 24
8023.2.ek $$\chi_{8023}(492, \cdot)$$ n/a 21824 32
8023.2.em $$\chi_{8023}(378, \cdot)$$ n/a 32736 48
8023.2.ep $$\chi_{8023}(23, \cdot)$$ n/a 32736 48
8023.2.eq $$\chi_{8023}(39, \cdot)$$ n/a 32736 48
8023.2.er $$\chi_{8023}(183, \cdot)$$ n/a 32736 48
8023.2.es $$\chi_{8023}(247, \cdot)$$ n/a 32736 48
8023.2.et $$\chi_{8023}(70, \cdot)$$ n/a 32736 48
8023.2.eu $$\chi_{8023}(381, \cdot)$$ n/a 32736 48
8023.2.fb $$\chi_{8023}(34, \cdot)$$ n/a 32736 48
8023.2.fd $$\chi_{8023}(2, \cdot)$$ n/a 32736 48
8023.2.fe $$\chi_{8023}(286, \cdot)$$ n/a 32736 48
8023.2.fl $$\chi_{8023}(15, \cdot)$$ n/a 32736 48
8023.2.fm $$\chi_{8023}(57, \cdot)$$ n/a 32736 48
8023.2.fn $$\chi_{8023}(60, \cdot)$$ n/a 32736 48
8023.2.fo $$\chi_{8023}(145, \cdot)$$ n/a 32736 48
8023.2.fp $$\chi_{8023}(81, \cdot)$$ n/a 32736 48
8023.2.fq $$\chi_{8023}(121, \cdot)$$ n/a 32736 48
8023.2.fs $$\chi_{8023}(50, \cdot)$$ n/a 65472 96
8023.2.fz $$\chi_{8023}(144, \cdot)$$ n/a 65472 96
8023.2.ga $$\chi_{8023}(154, \cdot)$$ n/a 65472 96
8023.2.gb $$\chi_{8023}(9, \cdot)$$ n/a 65472 96
8023.2.gc $$\chi_{8023}(36, \cdot)$$ n/a 65472 96
8023.2.gd $$\chi_{8023}(25, \cdot)$$ n/a 65472 96
8023.2.ge $$\chi_{8023}(18, \cdot)$$ n/a 65472 96
8023.2.gh $$\chi_{8023}(87, \cdot)$$ n/a 65472 96
8023.2.gi $$\chi_{8023}(130, \cdot)$$ n/a 130944 192
8023.2.gp $$\chi_{8023}(35, \cdot)$$ n/a 130944 192
8023.2.gq $$\chi_{8023}(21, \cdot)$$ n/a 130944 192
8023.2.gr $$\chi_{8023}(68, \cdot)$$ n/a 130944 192
8023.2.gs $$\chi_{8023}(17, \cdot)$$ n/a 130944 192
8023.2.gt $$\chi_{8023}(55, \cdot)$$ n/a 130944 192
8023.2.gu $$\chi_{8023}(132, \cdot)$$ n/a 130944 192
8023.2.gx $$\chi_{8023}(123, \cdot)$$ n/a 130944 192

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8023))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8023)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(71))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(113))$$$$^{\oplus 2}$$