# Properties

 Label 6019.2 Level 6019 Weight 2 Dimension 1.47762e+06 Nonzero newspaces 60 Sturm bound 6.0023e+06

## Defining parameters

 Level: $$N$$ = $$6019 = 13 \cdot 463$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$6002304$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6019))$$.

Total New Old
Modular forms 1506120 1487769 18351
Cusp forms 1495033 1477625 17408
Eisenstein series 11087 10144 943

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6019))$$

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
6019.2.a $$\chi_{6019}(1, \cdot)$$ 6019.2.a.a 1 1
6019.2.a.b 101
6019.2.a.c 108
6019.2.a.d 123
6019.2.a.e 130
6019.2.c $$\chi_{6019}(1390, \cdot)$$ n/a 538 1
6019.2.e $$\chi_{6019}(484, \cdot)$$ n/a 1078 2
6019.2.f $$\chi_{6019}(1873, \cdot)$$ n/a 928 2
6019.2.g $$\chi_{6019}(464, \cdot)$$ n/a 1080 2
6019.2.h $$\chi_{6019}(2336, \cdot)$$ n/a 1078 2
6019.2.i $$\chi_{6019}(1851, \cdot)$$ n/a 1076 2
6019.2.l $$\chi_{6019}(1830, \cdot)$$ n/a 1078 2
6019.2.p $$\chi_{6019}(927, \cdot)$$ n/a 1076 2
6019.2.q $$\chi_{6019}(441, \cdot)$$ n/a 1080 2
6019.2.r $$\chi_{6019}(4651, \cdot)$$ n/a 1078 2
6019.2.w $$\chi_{6019}(118, \cdot)$$ n/a 2784 6
6019.2.x $$\chi_{6019}(1288, \cdot)$$ n/a 4640 10
6019.2.y $$\chi_{6019}(1874, \cdot)$$ n/a 2156 4
6019.2.bc $$\chi_{6019}(462, \cdot)$$ n/a 2160 4
6019.2.bd $$\chi_{6019}(1411, \cdot)$$ n/a 2156 4
6019.2.be $$\chi_{6019}(905, \cdot)$$ n/a 2160 4
6019.2.bh $$\chi_{6019}(1156, \cdot)$$ n/a 3228 6
6019.2.bj $$\chi_{6019}(653, \cdot)$$ n/a 6468 12
6019.2.bk $$\chi_{6019}(230, \cdot)$$ n/a 6480 12
6019.2.bl $$\chi_{6019}(196, \cdot)$$ n/a 5568 12
6019.2.bm $$\chi_{6019}(178, \cdot)$$ n/a 6468 12
6019.2.bo $$\chi_{6019}(337, \cdot)$$ n/a 5380 10
6019.2.br $$\chi_{6019}(177, \cdot)$$ n/a 6456 12
6019.2.bs $$\chi_{6019}(133, \cdot)$$ n/a 10780 20
6019.2.bt $$\chi_{6019}(55, \cdot)$$ n/a 10800 20
6019.2.bu $$\chi_{6019}(833, \cdot)$$ n/a 9280 20
6019.2.bv $$\chi_{6019}(68, \cdot)$$ n/a 10780 20
6019.2.ca $$\chi_{6019}(641, \cdot)$$ n/a 6468 12
6019.2.cb $$\chi_{6019}(714, \cdot)$$ n/a 6480 12
6019.2.cc $$\chi_{6019}(693, \cdot)$$ n/a 6480 12
6019.2.cg $$\chi_{6019}(251, \cdot)$$ n/a 6468 12
6019.2.cj $$\chi_{6019}(216, \cdot)$$ n/a 10760 20
6019.2.co $$\chi_{6019}(36, \cdot)$$ n/a 10780 20
6019.2.cp $$\chi_{6019}(77, \cdot)$$ n/a 10800 20
6019.2.cq $$\chi_{6019}(134, \cdot)$$ n/a 10800 20
6019.2.cu $$\chi_{6019}(95, \cdot)$$ n/a 10780 20
6019.2.cw $$\chi_{6019}(66, \cdot)$$ n/a 27840 60
6019.2.cy $$\chi_{6019}(281, \cdot)$$ n/a 12960 24
6019.2.cz $$\chi_{6019}(145, \cdot)$$ n/a 12936 24
6019.2.da $$\chi_{6019}(345, \cdot)$$ n/a 12960 24
6019.2.de $$\chi_{6019}(730, \cdot)$$ n/a 12936 24
6019.2.dg $$\chi_{6019}(148, \cdot)$$ n/a 21600 40
6019.2.dh $$\chi_{6019}(305, \cdot)$$ n/a 21600 40
6019.2.di $$\chi_{6019}(6, \cdot)$$ n/a 21560 40
6019.2.dm $$\chi_{6019}(93, \cdot)$$ n/a 21560 40
6019.2.do $$\chi_{6019}(64, \cdot)$$ n/a 32280 60
6019.2.dq $$\chi_{6019}(9, \cdot)$$ n/a 64680 120
6019.2.dr $$\chi_{6019}(79, \cdot)$$ n/a 55680 120
6019.2.ds $$\chi_{6019}(100, \cdot)$$ n/a 64800 120
6019.2.dt $$\chi_{6019}(29, \cdot)$$ n/a 64680 120
6019.2.du $$\chi_{6019}(44, \cdot)$$ n/a 64560 120
6019.2.dx $$\chi_{6019}(30, \cdot)$$ n/a 64680 120
6019.2.eb $$\chi_{6019}(49, \cdot)$$ n/a 64800 120
6019.2.ec $$\chi_{6019}(25, \cdot)$$ n/a 64800 120
6019.2.ed $$\chi_{6019}(4, \cdot)$$ n/a 64680 120
6019.2.ei $$\chi_{6019}(20, \cdot)$$ n/a 129360 240
6019.2.em $$\chi_{6019}(11, \cdot)$$ n/a 129360 240
6019.2.en $$\chi_{6019}(7, \cdot)$$ n/a 129600 240
6019.2.eo $$\chi_{6019}(5, \cdot)$$ n/a 129600 240

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6019))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6019)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(463))$$$$^{\oplus 2}$$