Properties

 Label 4020.2 Level 4020 Weight 2 Dimension 171928 Nonzero newspaces 48 Sturm bound 1.72339e+06

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

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