Properties

 Label 6031.2 Level 6031 Weight 2 Dimension 1.50641e+06 Nonzero newspaces 105 Sturm bound 6.0575e+06

Defining parameters

 Level: $$N$$ = $$6031 = 37 \cdot 163$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$105$$ Sturm bound: $$6057504$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6031))$$.

Total New Old
Modular forms 1520208 1517683 2525
Cusp forms 1508545 1506411 2134
Eisenstein series 11663 11272 391

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6031))$$

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
6031.2.a $$\chi_{6031}(1, \cdot)$$ 6031.2.a.a 1 1
6031.2.a.b 109
6031.2.a.c 110
6031.2.a.d 133
6031.2.a.e 134
6031.2.c $$\chi_{6031}(4402, \cdot)$$ n/a 512 1
6031.2.e $$\chi_{6031}(1305, \cdot)$$ n/a 1028 2
6031.2.f $$\chi_{6031}(2875, \cdot)$$ n/a 1032 2
6031.2.g $$\chi_{6031}(593, \cdot)$$ n/a 984 2
6031.2.h $$\chi_{6031}(1897, \cdot)$$ n/a 1032 2
6031.2.j $$\chi_{6031}(1955, \cdot)$$ n/a 1032 2
6031.2.l $$\chi_{6031}(3690, \cdot)$$ n/a 1032 2
6031.2.p $$\chi_{6031}(221, \cdot)$$ n/a 1032 2
6031.2.q $$\chi_{6031}(2120, \cdot)$$ n/a 1024 2
6031.2.r $$\chi_{6031}(2712, \cdot)$$ n/a 1032 2
6031.2.w $$\chi_{6031}(366, \cdot)$$ n/a 3108 6
6031.2.x $$\chi_{6031}(1181, \cdot)$$ n/a 3108 6
6031.2.y $$\chi_{6031}(248, \cdot)$$ n/a 3096 6
6031.2.z $$\chi_{6031}(38, \cdot)$$ n/a 2952 6
6031.2.ba $$\chi_{6031}(2972, \cdot)$$ n/a 3108 6
6031.2.bb $$\chi_{6031}(201, \cdot)$$ n/a 3108 6
6031.2.bc $$\chi_{6031}(303, \cdot)$$ n/a 3108 6
6031.2.bd $$\chi_{6031}(164, \cdot)$$ n/a 3084 6
6031.2.be $$\chi_{6031}(2014, \cdot)$$ n/a 3108 6
6031.2.bf $$\chi_{6031}(710, \cdot)$$ n/a 3108 6
6031.2.bg $$\chi_{6031}(1342, \cdot)$$ n/a 3096 6
6031.2.bh $$\chi_{6031}(53, \cdot)$$ n/a 3108 6
6031.2.bj $$\chi_{6031}(711, \cdot)$$ n/a 2064 4
6031.2.bk $$\chi_{6031}(105, \cdot)$$ n/a 2064 4
6031.2.bl $$\chi_{6031}(162, \cdot)$$ n/a 2064 4
6031.2.bp $$\chi_{6031}(874, \cdot)$$ n/a 2064 4
6031.2.bq $$\chi_{6031}(411, \cdot)$$ n/a 3108 6
6031.2.bv $$\chi_{6031}(1063, \cdot)$$ n/a 3096 6
6031.2.cb $$\chi_{6031}(58, \cdot)$$ n/a 3108 6
6031.2.cc $$\chi_{6031}(1468, \cdot)$$ n/a 3072 6
6031.2.cd $$\chi_{6031}(1362, \cdot)$$ n/a 3108 6
6031.2.ci $$\chi_{6031}(622, \cdot)$$ n/a 3108 6
6031.2.cj $$\chi_{6031}(1505, \cdot)$$ n/a 3108 6
6031.2.cm $$\chi_{6031}(955, \cdot)$$ n/a 3108 6
6031.2.cs $$\chi_{6031}(85, \cdot)$$ n/a 3096 6
6031.2.ct $$\chi_{6031}(2367, \cdot)$$ n/a 3096 6
6031.2.cw $$\chi_{6031}(855, \cdot)$$ n/a 3108 6
6031.2.cy $$\chi_{6031}(40, \cdot)$$ n/a 3108 6
6031.2.da $$\chi_{6031}(810, \cdot)$$ n/a 9324 18
6031.2.db $$\chi_{6031}(441, \cdot)$$ n/a 9324 18
6031.2.dc $$\chi_{6031}(778, \cdot)$$ n/a 8856 18
6031.2.dd $$\chi_{6031}(158, \cdot)$$ n/a 9288 18
6031.2.de $$\chi_{6031}(787, \cdot)$$ n/a 9288 18
6031.2.df $$\chi_{6031}(514, \cdot)$$ n/a 9324 18
6031.2.dg $$\chi_{6031}(155, \cdot)$$ n/a 9324 18
6031.2.dh $$\chi_{6031}(604, \cdot)$$ n/a 9324 18
6031.2.di $$\chi_{6031}(1163, \cdot)$$ n/a 9324 18
6031.2.dk $$\chi_{6031}(449, \cdot)$$ n/a 6216 12
6031.2.dl $$\chi_{6031}(241, \cdot)$$ n/a 6216 12
6031.2.dm $$\chi_{6031}(775, \cdot)$$ n/a 6216 12
6031.2.dp $$\chi_{6031}(651, \cdot)$$ n/a 6216 12
6031.2.dq $$\chi_{6031}(594, \cdot)$$ n/a 6216 12
6031.2.dt $$\chi_{6031}(125, \cdot)$$ n/a 6192 12
6031.2.dv $$\chi_{6031}(23, \cdot)$$ n/a 6192 12
6031.2.dw $$\chi_{6031}(512, \cdot)$$ n/a 6192 12
6031.2.ea $$\chi_{6031}(59, \cdot)$$ n/a 6216 12
6031.2.eb $$\chi_{6031}(838, \cdot)$$ n/a 6216 12
6031.2.ec $$\chi_{6031}(612, \cdot)$$ n/a 6216 12
6031.2.eg $$\chi_{6031}(893, \cdot)$$ n/a 6216 12
6031.2.ei $$\chi_{6031}(115, \cdot)$$ n/a 9324 18
6031.2.em $$\chi_{6031}(136, \cdot)$$ n/a 9324 18
6031.2.en $$\chi_{6031}(77, \cdot)$$ n/a 9324 18
6031.2.ep $$\chi_{6031}(132, \cdot)$$ n/a 9324 18
6031.2.ev $$\chi_{6031}(36, \cdot)$$ n/a 9288 18
6031.2.ew $$\chi_{6031}(64, \cdot)$$ n/a 9288 18
6031.2.ez $$\chi_{6031}(788, \cdot)$$ n/a 9288 18
6031.2.fd $$\chi_{6031}(21, \cdot)$$ n/a 9324 18
6031.2.fg $$\chi_{6031}(65, \cdot)$$ n/a 9324 18
6031.2.fi $$\chi_{6031}(416, \cdot)$$ n/a 27918 54
6031.2.fj $$\chi_{6031}(33, \cdot)$$ n/a 27918 54
6031.2.fk $$\chi_{6031}(46, \cdot)$$ n/a 27918 54
6031.2.fl $$\chi_{6031}(16, \cdot)$$ n/a 27918 54
6031.2.fm $$\chi_{6031}(223, \cdot)$$ n/a 26568 54
6031.2.fn $$\chi_{6031}(10, \cdot)$$ n/a 27972 54
6031.2.fo $$\chi_{6031}(26, \cdot)$$ n/a 27972 54
6031.2.fp $$\chi_{6031}(9, \cdot)$$ n/a 27918 54
6031.2.fq $$\chi_{6031}(34, \cdot)$$ n/a 27918 54
6031.2.fs $$\chi_{6031}(13, \cdot)$$ n/a 18648 36
6031.2.fu $$\chi_{6031}(8, \cdot)$$ n/a 18576 36
6031.2.fv $$\chi_{6031}(31, \cdot)$$ n/a 18576 36
6031.2.fw $$\chi_{6031}(320, \cdot)$$ n/a 18648 36
6031.2.fz $$\chi_{6031}(200, \cdot)$$ n/a 18648 36
6031.2.gb $$\chi_{6031}(98, \cdot)$$ n/a 18648 36
6031.2.ge $$\chi_{6031}(171, \cdot)$$ n/a 18576 36
6031.2.gf $$\chi_{6031}(357, \cdot)$$ n/a 18648 36
6031.2.gg $$\chi_{6031}(5, \cdot)$$ n/a 18648 36
6031.2.gl $$\chi_{6031}(41, \cdot)$$ n/a 27918 54
6031.2.gm $$\chi_{6031}(225, \cdot)$$ n/a 27918 54
6031.2.gn $$\chi_{6031}(250, \cdot)$$ n/a 27918 54
6031.2.gs $$\chi_{6031}(4, \cdot)$$ n/a 27918 54
6031.2.gu $$\chi_{6031}(307, \cdot)$$ n/a 27972 54
6031.2.gx $$\chi_{6031}(258, \cdot)$$ n/a 27972 54
6031.2.hb $$\chi_{6031}(196, \cdot)$$ n/a 27972 54
6031.2.hc $$\chi_{6031}(62, \cdot)$$ n/a 27918 54
6031.2.hj $$\chi_{6031}(151, \cdot)$$ n/a 27918 54
6031.2.hl $$\chi_{6031}(50, \cdot)$$ n/a 55836 108
6031.2.hm $$\chi_{6031}(42, \cdot)$$ n/a 55836 108
6031.2.hn $$\chi_{6031}(72, \cdot)$$ n/a 55836 108
6031.2.hp $$\chi_{6031}(45, \cdot)$$ n/a 55944 108
6031.2.hs $$\chi_{6031}(29, \cdot)$$ n/a 55944 108
6031.2.hu $$\chi_{6031}(68, \cdot)$$ n/a 55944 108
6031.2.hv $$\chi_{6031}(18, \cdot)$$ n/a 55836 108
6031.2.hy $$\chi_{6031}(2, \cdot)$$ n/a 55836 108
6031.2.ib $$\chi_{6031}(20, \cdot)$$ n/a 55836 108

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6031))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6031)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(163))$$$$^{\oplus 2}$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T^{2}$$)
$3$ ($$1 - 3 T + 3 T^{2}$$)
$5$ ($$1 - 4 T + 5 T^{2}$$)
$7$ ($$1 - T + 7 T^{2}$$)
$11$ ($$1 - T + 11 T^{2}$$)
$13$ ($$1 - 4 T + 13 T^{2}$$)
$17$ ($$1 + 2 T + 17 T^{2}$$)
$19$ ($$1 + 19 T^{2}$$)
$23$ ($$1 + 8 T + 23 T^{2}$$)
$29$ ($$1 + 29 T^{2}$$)
$31$ ($$1 - 2 T + 31 T^{2}$$)
$37$ ($$1 - T$$)
$41$ ($$1 - 3 T + 41 T^{2}$$)
$43$ ($$1 - 4 T + 43 T^{2}$$)
$47$ ($$1 + 9 T + 47 T^{2}$$)
$53$ ($$1 - 9 T + 53 T^{2}$$)
$59$ ($$1 + 6 T + 59 T^{2}$$)
$61$ ($$1 + 6 T + 61 T^{2}$$)
$67$ ($$1 - 8 T + 67 T^{2}$$)
$71$ ($$1 - 13 T + 71 T^{2}$$)
$73$ ($$1 - 5 T + 73 T^{2}$$)
$79$ ($$1 + 14 T + 79 T^{2}$$)
$83$ ($$1 - 9 T + 83 T^{2}$$)
$89$ ($$1 + 12 T + 89 T^{2}$$)
$97$ ($$1 - 12 T + 97 T^{2}$$)