# Properties

 Label 6017.2 Level 6017 Weight 2 Dimension 1.46619e+06 Nonzero newspaces 32 Sturm bound 5.98416e+06

## Defining parameters

 Level: $$N$$ = $$6017 = 11 \cdot 547$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$5984160$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6017))$$.

Total New Old
Modular forms 1501500 1476001 25499
Cusp forms 1490581 1466189 24392
Eisenstein series 10919 9812 1107

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6017))$$

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
6017.2.a $$\chi_{6017}(1, \cdot)$$ 6017.2.a.a 1 1
6017.2.a.b 1
6017.2.a.c 106
6017.2.a.d 107
6017.2.a.e 119
6017.2.a.f 121
6017.2.d $$\chi_{6017}(6016, \cdot)$$ n/a 546 1
6017.2.e $$\chi_{6017}(1134, \cdot)$$ n/a 912 2
6017.2.f $$\chi_{6017}(548, \cdot)$$ n/a 2184 4
6017.2.g $$\chi_{6017}(1682, \cdot)$$ n/a 1092 2
6017.2.j $$\chi_{6017}(628, \cdot)$$ n/a 2748 6
6017.2.k $$\chi_{6017}(546, \cdot)$$ n/a 2184 4
6017.2.n $$\chi_{6017}(353, \cdot)$$ n/a 5496 12
6017.2.o $$\chi_{6017}(538, \cdot)$$ n/a 3276 6
6017.2.r $$\chi_{6017}(587, \cdot)$$ n/a 4368 8
6017.2.s $$\chi_{6017}(716, \cdot)$$ n/a 5472 12
6017.2.t $$\chi_{6017}(197, \cdot)$$ n/a 6552 12
6017.2.y $$\chi_{6017}(41, \cdot)$$ n/a 4368 8
6017.2.z $$\chi_{6017}(9, \cdot)$$ n/a 13104 24
6017.2.ba $$\chi_{6017}(199, \cdot)$$ n/a 10944 24
6017.2.bd $$\chi_{6017}(120, \cdot)$$ n/a 6552 12
6017.2.be $$\chi_{6017}(350, \cdot)$$ n/a 26208 48
6017.2.bh $$\chi_{6017}(365, \cdot)$$ n/a 13104 24
6017.2.bk $$\chi_{6017}(692, \cdot)$$ n/a 13104 24
6017.2.bl $$\chi_{6017}(100, \cdot)$$ n/a 32976 72
6017.2.bm $$\chi_{6017}(14, \cdot)$$ n/a 26208 48
6017.2.bp $$\chi_{6017}(28, \cdot)$$ n/a 26208 48
6017.2.bs $$\chi_{6017}(65, \cdot)$$ n/a 39312 72
6017.2.bt $$\chi_{6017}(47, \cdot)$$ n/a 52416 96
6017.2.bu $$\chi_{6017}(39, \cdot)$$ n/a 26208 48
6017.2.bx $$\chi_{6017}(34, \cdot)$$ n/a 65664 144
6017.2.by $$\chi_{6017}(83, \cdot)$$ n/a 52416 96
6017.2.cb $$\chi_{6017}(64, \cdot)$$ n/a 157248 288
6017.2.cc $$\chi_{6017}(32, \cdot)$$ n/a 78624 144
6017.2.cf $$\chi_{6017}(8, \cdot)$$ n/a 157248 288
6017.2.ci $$\chi_{6017}(4, \cdot)$$ n/a 314496 576
6017.2.cl $$\chi_{6017}(2, \cdot)$$ n/a 314496 576

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6017))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6017)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(547))$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T^{2}$$)($$1 + 2 T^{2}$$)
$3$ ($$1 + 3 T^{2}$$)($$1 - 2 T + 3 T^{2}$$)
$5$ ($$1 + 5 T^{2}$$)($$1 - 4 T + 5 T^{2}$$)
$7$ ($$1 + 2 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)
$11$ ($$1 + T$$)($$1 - T$$)
$13$ ($$1 + 5 T + 13 T^{2}$$)($$1 - T + 13 T^{2}$$)
$17$ ($$1 + 4 T + 17 T^{2}$$)($$1 - 8 T + 17 T^{2}$$)
$19$ ($$1 + 7 T + 19 T^{2}$$)($$1 + 5 T + 19 T^{2}$$)
$23$ ($$1 - 2 T + 23 T^{2}$$)($$1 - 6 T + 23 T^{2}$$)
$29$ ($$1 + T + 29 T^{2}$$)($$1 - 5 T + 29 T^{2}$$)
$31$ ($$1 - 4 T + 31 T^{2}$$)($$1 - 10 T + 31 T^{2}$$)
$37$ ($$1 + 6 T + 37 T^{2}$$)($$1 + 37 T^{2}$$)
$41$ ($$1 - 2 T + 41 T^{2}$$)($$1 + 41 T^{2}$$)
$43$ ($$1 + 8 T + 43 T^{2}$$)($$1 + 10 T + 43 T^{2}$$)
$47$ ($$1 + 9 T + 47 T^{2}$$)($$1 + 9 T + 47 T^{2}$$)
$53$ ($$1 - 2 T + 53 T^{2}$$)($$1 + 10 T + 53 T^{2}$$)
$59$ ($$1 + 6 T + 59 T^{2}$$)($$1 + 14 T + 59 T^{2}$$)
$61$ ($$1 + 14 T + 61 T^{2}$$)($$1 + 14 T + 61 T^{2}$$)
$67$ ($$1 + 5 T + 67 T^{2}$$)($$1 + T + 67 T^{2}$$)
$71$ ($$1 - 10 T + 71 T^{2}$$)($$1 - 12 T + 71 T^{2}$$)
$73$ ($$1 + 6 T + 73 T^{2}$$)($$1 + 2 T + 73 T^{2}$$)
$79$ ($$1 + 6 T + 79 T^{2}$$)($$1 - 4 T + 79 T^{2}$$)
$83$ ($$1 - 4 T + 83 T^{2}$$)($$1 - 6 T + 83 T^{2}$$)
$89$ ($$1 - 8 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)
$97$ ($$1 - 15 T + 97 T^{2}$$)($$1 + 13 T + 97 T^{2}$$)