Properties

Label 8023.2
Level 8023
Weight 2
Dimension 2672135
Nonzero newspaces 90
Sturm bound 10725120

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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

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