Properties

Label 8040.2
Level 8040
Weight 2
Dimension 664612
Nonzero newspaces 72
Sturm bound 6893568

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Defining parameters

Level: \( N \) = \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(6893568\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8040))\).

Total New Old
Modular forms 1736064 667732 1068332
Cusp forms 1710721 664612 1046109
Eisenstein series 25343 3120 22223

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8040))\)

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
8040.2.a \(\chi_{8040}(1, \cdot)\) 8040.2.a.a 1 1
8040.2.a.b 1
8040.2.a.c 1
8040.2.a.d 1
8040.2.a.e 1
8040.2.a.f 1
8040.2.a.g 1
8040.2.a.h 1
8040.2.a.i 1
8040.2.a.j 1
8040.2.a.k 1
8040.2.a.l 1
8040.2.a.m 2
8040.2.a.n 5
8040.2.a.o 5
8040.2.a.p 5
8040.2.a.q 6
8040.2.a.r 6
8040.2.a.s 6
8040.2.a.t 7
8040.2.a.u 8
8040.2.a.v 8
8040.2.a.w 8
8040.2.a.x 8
8040.2.a.y 9
8040.2.a.z 9
8040.2.a.ba 9
8040.2.a.bb 9
8040.2.a.bc 10
8040.2.b \(\chi_{8040}(1339, \cdot)\) n/a 816 1
8040.2.c \(\chi_{8040}(4691, \cdot)\) n/a 1056 1
8040.2.f \(\chi_{8040}(5629, \cdot)\) n/a 792 1
8040.2.g \(\chi_{8040}(4421, \cdot)\) n/a 1088 1
8040.2.j \(\chi_{8040}(401, \cdot)\) n/a 272 1
8040.2.k \(\chi_{8040}(1609, \cdot)\) n/a 200 1
8040.2.n \(\chi_{8040}(671, \cdot)\) None 0 1
8040.2.o \(\chi_{8040}(5359, \cdot)\) None 0 1
8040.2.t \(\chi_{8040}(4021, \cdot)\) n/a 528 1
8040.2.u \(\chi_{8040}(6029, \cdot)\) n/a 1624 1
8040.2.x \(\chi_{8040}(7771, \cdot)\) n/a 544 1
8040.2.y \(\chi_{8040}(6299, \cdot)\) n/a 1584 1
8040.2.bb \(\chi_{8040}(2279, \cdot)\) None 0 1
8040.2.bc \(\chi_{8040}(3751, \cdot)\) None 0 1
8040.2.bf \(\chi_{8040}(2009, \cdot)\) n/a 408 1
8040.2.bg \(\chi_{8040}(841, \cdot)\) n/a 272 2
8040.2.bh \(\chi_{8040}(937, \cdot)\) n/a 408 2
8040.2.bk \(\chi_{8040}(1073, \cdot)\) n/a 792 2
8040.2.bm \(\chi_{8040}(1207, \cdot)\) None 0 2
8040.2.bn \(\chi_{8040}(1607, \cdot)\) None 0 2
8040.2.bq \(\chi_{8040}(803, \cdot)\) n/a 3248 2
8040.2.br \(\chi_{8040}(403, \cdot)\) n/a 1584 2
8040.2.bt \(\chi_{8040}(1877, \cdot)\) n/a 3168 2
8040.2.bw \(\chi_{8040}(133, \cdot)\) n/a 1632 2
8040.2.bx \(\chi_{8040}(1169, \cdot)\) n/a 816 2
8040.2.ca \(\chi_{8040}(2911, \cdot)\) None 0 2
8040.2.cb \(\chi_{8040}(2039, \cdot)\) None 0 2
8040.2.ce \(\chi_{8040}(6059, \cdot)\) n/a 3248 2
8040.2.cf \(\chi_{8040}(6931, \cdot)\) n/a 1088 2
8040.2.ci \(\chi_{8040}(5189, \cdot)\) n/a 3248 2
8040.2.cj \(\chi_{8040}(3781, \cdot)\) n/a 1088 2
8040.2.co \(\chi_{8040}(4519, \cdot)\) None 0 2
8040.2.cp \(\chi_{8040}(431, \cdot)\) None 0 2
8040.2.cs \(\chi_{8040}(1369, \cdot)\) n/a 408 2
8040.2.ct \(\chi_{8040}(641, \cdot)\) n/a 544 2
8040.2.cw \(\chi_{8040}(3581, \cdot)\) n/a 2176 2
8040.2.cx \(\chi_{8040}(5389, \cdot)\) n/a 1632 2
8040.2.da \(\chi_{8040}(4451, \cdot)\) n/a 2176 2
8040.2.db \(\chi_{8040}(499, \cdot)\) n/a 1632 2
8040.2.dc \(\chi_{8040}(241, \cdot)\) n/a 1360 10
8040.2.de \(\chi_{8040}(373, \cdot)\) n/a 3264 4
8040.2.df \(\chi_{8040}(1637, \cdot)\) n/a 6496 4
8040.2.dh \(\chi_{8040}(163, \cdot)\) n/a 3264 4
8040.2.dk \(\chi_{8040}(1043, \cdot)\) n/a 6496 4
8040.2.dl \(\chi_{8040}(767, \cdot)\) None 0 4
8040.2.do \(\chi_{8040}(967, \cdot)\) None 0 4
8040.2.dq \(\chi_{8040}(833, \cdot)\) n/a 1632 4
8040.2.dr \(\chi_{8040}(97, \cdot)\) n/a 816 4
8040.2.dt \(\chi_{8040}(209, \cdot)\) n/a 4080 10
8040.2.dw \(\chi_{8040}(359, \cdot)\) None 0 10
8040.2.dx \(\chi_{8040}(271, \cdot)\) None 0 10
8040.2.ea \(\chi_{8040}(1651, \cdot)\) n/a 5440 10
8040.2.eb \(\chi_{8040}(59, \cdot)\) n/a 16240 10
8040.2.ee \(\chi_{8040}(2101, \cdot)\) n/a 5440 10
8040.2.ef \(\chi_{8040}(2189, \cdot)\) n/a 16240 10
8040.2.ek \(\chi_{8040}(551, \cdot)\) None 0 10
8040.2.el \(\chi_{8040}(1519, \cdot)\) None 0 10
8040.2.eo \(\chi_{8040}(161, \cdot)\) n/a 2720 10
8040.2.ep \(\chi_{8040}(1489, \cdot)\) n/a 2040 10
8040.2.es \(\chi_{8040}(349, \cdot)\) n/a 8160 10
8040.2.et \(\chi_{8040}(581, \cdot)\) n/a 10880 10
8040.2.ew \(\chi_{8040}(139, \cdot)\) n/a 8160 10
8040.2.ex \(\chi_{8040}(131, \cdot)\) n/a 10880 10
8040.2.ey \(\chi_{8040}(121, \cdot)\) n/a 2720 20
8040.2.fa \(\chi_{8040}(293, \cdot)\) n/a 32480 20
8040.2.fb \(\chi_{8040}(253, \cdot)\) n/a 16320 20
8040.2.fd \(\chi_{8040}(563, \cdot)\) n/a 32480 20
8040.2.fg \(\chi_{8040}(283, \cdot)\) n/a 16320 20
8040.2.fh \(\chi_{8040}(223, \cdot)\) None 0 20
8040.2.fk \(\chi_{8040}(407, \cdot)\) None 0 20
8040.2.fm \(\chi_{8040}(313, \cdot)\) n/a 4080 20
8040.2.fn \(\chi_{8040}(617, \cdot)\) n/a 8160 20
8040.2.fp \(\chi_{8040}(371, \cdot)\) n/a 21760 20
8040.2.fq \(\chi_{8040}(379, \cdot)\) n/a 16320 20
8040.2.ft \(\chi_{8040}(101, \cdot)\) n/a 21760 20
8040.2.fu \(\chi_{8040}(709, \cdot)\) n/a 16320 20
8040.2.fx \(\chi_{8040}(49, \cdot)\) n/a 4080 20
8040.2.fy \(\chi_{8040}(41, \cdot)\) n/a 5440 20
8040.2.gb \(\chi_{8040}(79, \cdot)\) None 0 20
8040.2.gc \(\chi_{8040}(71, \cdot)\) None 0 20
8040.2.gh \(\chi_{8040}(749, \cdot)\) n/a 32480 20
8040.2.gi \(\chi_{8040}(181, \cdot)\) n/a 10880 20
8040.2.gl \(\chi_{8040}(419, \cdot)\) n/a 32480 20
8040.2.gm \(\chi_{8040}(331, \cdot)\) n/a 10880 20
8040.2.gp \(\chi_{8040}(31, \cdot)\) None 0 20
8040.2.gq \(\chi_{8040}(479, \cdot)\) None 0 20
8040.2.gt \(\chi_{8040}(329, \cdot)\) n/a 8160 20
8040.2.gu \(\chi_{8040}(17, \cdot)\) n/a 16320 40
8040.2.gx \(\chi_{8040}(337, \cdot)\) n/a 8160 40
8040.2.gz \(\chi_{8040}(383, \cdot)\) None 0 40
8040.2.ha \(\chi_{8040}(103, \cdot)\) None 0 40
8040.2.hd \(\chi_{8040}(307, \cdot)\) n/a 32640 40
8040.2.he \(\chi_{8040}(203, \cdot)\) n/a 64960 40
8040.2.hg \(\chi_{8040}(13, \cdot)\) n/a 32640 40
8040.2.hj \(\chi_{8040}(77, \cdot)\) n/a 64960 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(402))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(536))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(670))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(804))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1005))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1340))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2010))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4020))\)\(^{\oplus 2}\)