Properties

Label 4020.2
Level 4020
Weight 2
Dimension 171928
Nonzero newspaces 48
Sturm bound 1723392

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Defining parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(1723392\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4020))\).

Total New Old
Modular forms 436128 173496 262632
Cusp forms 425569 171928 253641
Eisenstein series 10559 1568 8991

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4020))\)

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
4020.2.a \(\chi_{4020}(1, \cdot)\) 4020.2.a.a 1 1
4020.2.a.b 4
4020.2.a.c 4
4020.2.a.d 4
4020.2.a.e 5
4020.2.a.f 6
4020.2.a.g 6
4020.2.a.h 7
4020.2.a.i 7
4020.2.f \(\chi_{4020}(401, \cdot)\) 4020.2.f.a 46 1
4020.2.f.b 46
4020.2.g \(\chi_{4020}(1609, \cdot)\) 4020.2.g.a 2 1
4020.2.g.b 24
4020.2.g.c 38
4020.2.h \(\chi_{4020}(671, \cdot)\) n/a 528 1
4020.2.i \(\chi_{4020}(1339, \cdot)\) n/a 408 1
4020.2.n \(\chi_{4020}(2279, \cdot)\) n/a 792 1
4020.2.o \(\chi_{4020}(3751, \cdot)\) n/a 272 1
4020.2.p \(\chi_{4020}(2009, \cdot)\) n/a 136 1
4020.2.q \(\chi_{4020}(841, \cdot)\) 4020.2.q.a 2 2
4020.2.q.b 2
4020.2.q.c 2
4020.2.q.d 2
4020.2.q.e 2
4020.2.q.f 2
4020.2.q.g 2
4020.2.q.h 2
4020.2.q.i 4
4020.2.q.j 12
4020.2.q.k 14
4020.2.q.l 22
4020.2.q.m 24
4020.2.r \(\chi_{4020}(133, \cdot)\) n/a 136 2
4020.2.s \(\chi_{4020}(1073, \cdot)\) n/a 264 2
4020.2.t \(\chi_{4020}(403, \cdot)\) n/a 792 2
4020.2.u \(\chi_{4020}(803, \cdot)\) n/a 1616 2
4020.2.z \(\chi_{4020}(1169, \cdot)\) n/a 272 2
4020.2.ba \(\chi_{4020}(2911, \cdot)\) n/a 544 2
4020.2.bb \(\chi_{4020}(2039, \cdot)\) n/a 1616 2
4020.2.bg \(\chi_{4020}(499, \cdot)\) n/a 816 2
4020.2.bh \(\chi_{4020}(431, \cdot)\) n/a 1088 2
4020.2.bi \(\chi_{4020}(1369, \cdot)\) n/a 136 2
4020.2.bj \(\chi_{4020}(641, \cdot)\) n/a 180 2
4020.2.bo \(\chi_{4020}(241, \cdot)\) n/a 440 10
4020.2.bt \(\chi_{4020}(767, \cdot)\) n/a 3232 4
4020.2.bu \(\chi_{4020}(163, \cdot)\) n/a 1632 4
4020.2.bv \(\chi_{4020}(833, \cdot)\) n/a 544 4
4020.2.bw \(\chi_{4020}(97, \cdot)\) n/a 272 4
4020.2.bx \(\chi_{4020}(209, \cdot)\) n/a 1360 10
4020.2.by \(\chi_{4020}(59, \cdot)\) n/a 8080 10
4020.2.bz \(\chi_{4020}(271, \cdot)\) n/a 2720 10
4020.2.ce \(\chi_{4020}(131, \cdot)\) n/a 5440 10
4020.2.cf \(\chi_{4020}(139, \cdot)\) n/a 4080 10
4020.2.cg \(\chi_{4020}(161, \cdot)\) n/a 920 10
4020.2.ch \(\chi_{4020}(349, \cdot)\) n/a 680 10
4020.2.cm \(\chi_{4020}(121, \cdot)\) n/a 920 20
4020.2.cr \(\chi_{4020}(223, \cdot)\) n/a 8160 20
4020.2.cs \(\chi_{4020}(407, \cdot)\) n/a 16160 20
4020.2.ct \(\chi_{4020}(253, \cdot)\) n/a 1360 20
4020.2.cu \(\chi_{4020}(293, \cdot)\) n/a 2720 20
4020.2.cz \(\chi_{4020}(49, \cdot)\) n/a 1360 20
4020.2.da \(\chi_{4020}(41, \cdot)\) n/a 1800 20
4020.2.db \(\chi_{4020}(79, \cdot)\) n/a 8160 20
4020.2.dc \(\chi_{4020}(71, \cdot)\) n/a 10880 20
4020.2.dh \(\chi_{4020}(31, \cdot)\) n/a 5440 20
4020.2.di \(\chi_{4020}(419, \cdot)\) n/a 16160 20
4020.2.dj \(\chi_{4020}(329, \cdot)\) n/a 2720 20
4020.2.dk \(\chi_{4020}(17, \cdot)\) n/a 5440 40
4020.2.dl \(\chi_{4020}(13, \cdot)\) n/a 2720 40
4020.2.dm \(\chi_{4020}(203, \cdot)\) n/a 32320 40
4020.2.dn \(\chi_{4020}(103, \cdot)\) n/a 16320 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4020))\) into lower level spaces

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