# Properties

 Label 6013.2 Level 6013 Weight 2 Dimension 1.40998e+06 Nonzero newspaces 40 Sturm bound 5.90304e+06

## Defining parameters

 Level: $$N$$ = $$6013 = 7 \cdot 859$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$5903040$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6013))$$.

Total New Old
Modular forms 1480908 1418551 62357
Cusp forms 1470613 1409979 60634
Eisenstein series 10295 8572 1723

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6013))$$

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
6013.2.a $$\chi_{6013}(1, \cdot)$$ 6013.2.a.a 1 1
6013.2.a.b 1
6013.2.a.c 104
6013.2.a.d 104
6013.2.a.e 109
6013.2.a.f 110
6013.2.c $$\chi_{6013}(6012, \cdot)$$ n/a 570 1
6013.2.e $$\chi_{6013}(1719, \cdot)$$ n/a 1144 2
6013.2.f $$\chi_{6013}(260, \cdot)$$ n/a 860 2
6013.2.g $$\chi_{6013}(1978, \cdot)$$ n/a 1142 2
6013.2.h $$\chi_{6013}(2837, \cdot)$$ n/a 1142 2
6013.2.j $$\chi_{6013}(2838, \cdot)$$ n/a 1142 2
6013.2.n $$\chi_{6013}(1979, \cdot)$$ n/a 1142 2
6013.2.o $$\chi_{6013}(3435, \cdot)$$ n/a 1144 2
6013.2.p $$\chi_{6013}(4556, \cdot)$$ n/a 1144 2
6013.2.u $$\chi_{6013}(169, \cdot)$$ n/a 4300 10
6013.2.v $$\chi_{6013}(463, \cdot)$$ n/a 5160 12
6013.2.x $$\chi_{6013}(846, \cdot)$$ n/a 5700 10
6013.2.ba $$\chi_{6013}(335, \cdot)$$ n/a 6840 12
6013.2.bc $$\chi_{6013}(46, \cdot)$$ n/a 11420 20
6013.2.bd $$\chi_{6013}(361, \cdot)$$ n/a 11420 20
6013.2.be $$\chi_{6013}(88, \cdot)$$ n/a 11440 20
6013.2.bf $$\chi_{6013}(43, \cdot)$$ n/a 8600 20
6013.2.bg $$\chi_{6013}(144, \cdot)$$ n/a 13704 24
6013.2.bh $$\chi_{6013}(277, \cdot)$$ n/a 13704 24
6013.2.bi $$\chi_{6013}(120, \cdot)$$ n/a 10320 24
6013.2.bj $$\chi_{6013}(100, \cdot)$$ n/a 13728 24
6013.2.bo $$\chi_{6013}(66, \cdot)$$ n/a 11440 20
6013.2.bp $$\chi_{6013}(195, \cdot)$$ n/a 11440 20
6013.2.bq $$\chi_{6013}(19, \cdot)$$ n/a 11420 20
6013.2.bu $$\chi_{6013}(313, \cdot)$$ n/a 11420 20
6013.2.ca $$\chi_{6013}(629, \cdot)$$ n/a 13728 24
6013.2.cb $$\chi_{6013}(10, \cdot)$$ n/a 13728 24
6013.2.cc $$\chi_{6013}(402, \cdot)$$ n/a 13704 24
6013.2.cg $$\chi_{6013}(12, \cdot)$$ n/a 13704 24
6013.2.ci $$\chi_{6013}(36, \cdot)$$ n/a 51600 120
6013.2.ck $$\chi_{6013}(27, \cdot)$$ n/a 68400 120
6013.2.cm $$\chi_{6013}(22, \cdot)$$ n/a 103200 240
6013.2.cn $$\chi_{6013}(74, \cdot)$$ n/a 137280 240
6013.2.co $$\chi_{6013}(25, \cdot)$$ n/a 137040 240
6013.2.cp $$\chi_{6013}(4, \cdot)$$ n/a 137040 240
6013.2.cr $$\chi_{6013}(3, \cdot)$$ n/a 137040 240
6013.2.cv $$\chi_{6013}(40, \cdot)$$ n/a 137040 240
6013.2.cw $$\chi_{6013}(55, \cdot)$$ n/a 137280 240
6013.2.cx $$\chi_{6013}(75, \cdot)$$ n/a 137280 240

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6013))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6013)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(859))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T + 2 T^{2}$$)($$1 - 2 T + 2 T^{2}$$)
$3$ ($$1 + 2 T + 3 T^{2}$$)($$1 + T + 3 T^{2}$$)
$5$ ($$1 + T + 5 T^{2}$$)($$1 + 5 T^{2}$$)
$7$ ($$1 - T$$)($$1 + T$$)
$11$ ($$1 + 11 T^{2}$$)($$1 + 11 T^{2}$$)
$13$ ($$1 + 2 T + 13 T^{2}$$)($$1 - 6 T + 13 T^{2}$$)
$17$ ($$1 + 3 T + 17 T^{2}$$)($$1 + 17 T^{2}$$)
$19$ ($$1 + 4 T + 19 T^{2}$$)($$1 - 4 T + 19 T^{2}$$)
$23$ ($$1 + 6 T + 23 T^{2}$$)($$1 + 2 T + 23 T^{2}$$)
$29$ ($$1 + 29 T^{2}$$)($$1 - 8 T + 29 T^{2}$$)
$31$ ($$1 + 9 T + 31 T^{2}$$)($$1 + 10 T + 31 T^{2}$$)
$37$ ($$1 - 2 T + 37 T^{2}$$)($$1 + 37 T^{2}$$)
$41$ ($$1 + 7 T + 41 T^{2}$$)($$1 - 2 T + 41 T^{2}$$)
$43$ ($$1 + 11 T + 43 T^{2}$$)($$1 - T + 43 T^{2}$$)
$47$ ($$1 - 4 T + 47 T^{2}$$)($$1 - 12 T + 47 T^{2}$$)
$53$ ($$1 + 13 T + 53 T^{2}$$)($$1 - 3 T + 53 T^{2}$$)
$59$ ($$1 + 9 T + 59 T^{2}$$)($$1 + 8 T + 59 T^{2}$$)
$61$ ($$1 - 11 T + 61 T^{2}$$)($$1 - 10 T + 61 T^{2}$$)
$67$ ($$1 + 2 T + 67 T^{2}$$)($$1 + 2 T + 67 T^{2}$$)
$71$ ($$1 + 71 T^{2}$$)($$1 - 8 T + 71 T^{2}$$)
$73$ ($$1 + 6 T + 73 T^{2}$$)($$1 + 9 T + 73 T^{2}$$)
$79$ ($$1 - 13 T + 79 T^{2}$$)($$1 - 15 T + 79 T^{2}$$)
$83$ ($$1 - 6 T + 83 T^{2}$$)($$1 - 15 T + 83 T^{2}$$)
$89$ ($$1 - 6 T + 89 T^{2}$$)($$1 + 7 T + 89 T^{2}$$)
$97$ ($$1 + 6 T + 97 T^{2}$$)($$1 - T + 97 T^{2}$$)