# Properties

 Label 8033.2 Level 8033 Weight 2 Dimension 2.67159e+06 Nonzero newspaces 48 Sturm bound 1.07419e+07

## Defining parameters

 Level: $$N$$ = $$8033\( 8033 = 29 \cdot 277$$ \) Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$10741920$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8033))$$.

Total New Old
Modular forms 2693208 2686441 6767
Cusp forms 2677753 2671589 6164
Eisenstein series 15455 14852 603

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8033))$$

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
8033.2.a $$\chi_{8033}(1, \cdot)$$ 8033.2.a.a 1 1
8033.2.a.b 153
8033.2.a.c 154
8033.2.a.d 168
8033.2.a.e 169
8033.2.b $$\chi_{8033}(4987, \cdot)$$ n/a 690 1
8033.2.c $$\chi_{8033}(3046, \cdot)$$ n/a 650 1
8033.2.d $$\chi_{8033}(8032, \cdot)$$ n/a 692 1
8033.2.e $$\chi_{8033}(2930, \cdot)$$ n/a 1296 2
8033.2.f $$\chi_{8033}(771, \cdot)$$ n/a 1386 2
8033.2.k $$\chi_{8033}(2830, \cdot)$$ n/a 1386 2
8033.2.l $$\chi_{8033}(117, \cdot)$$ n/a 1296 2
8033.2.m $$\chi_{8033}(2609, \cdot)$$ n/a 1388 2
8033.2.n $$\chi_{8033}(2377, \cdot)$$ n/a 1384 2
8033.2.o $$\chi_{8033}(832, \cdot)$$ n/a 4140 6
8033.2.p $$\chi_{8033}(1143, \cdot)$$ n/a 2772 4
8033.2.u $$\chi_{8033}(1844, \cdot)$$ n/a 2772 4
8033.2.v $$\chi_{8033}(1107, \cdot)$$ n/a 4152 6
8033.2.w $$\chi_{8033}(1938, \cdot)$$ n/a 4164 6
8033.2.x $$\chi_{8033}(555, \cdot)$$ n/a 4140 6
8033.2.y $$\chi_{8033}(393, \cdot)$$ n/a 8304 12
8033.2.z $$\chi_{8033}(30, \cdot)$$ n/a 14300 22
8033.2.ba $$\chi_{8033}(60, \cdot)$$ n/a 8316 12
8033.2.bf $$\chi_{8033}(217, \cdot)$$ n/a 8316 12
8033.2.bg $$\chi_{8033}(671, \cdot)$$ n/a 8304 12
8033.2.bh $$\chi_{8033}(991, \cdot)$$ n/a 8328 12
8033.2.bi $$\chi_{8033}(161, \cdot)$$ n/a 8328 12
8033.2.bj $$\chi_{8033}(318, \cdot)$$ n/a 15224 22
8033.2.bk $$\chi_{8033}(59, \cdot)$$ n/a 14300 22
8033.2.bl $$\chi_{8033}(434, \cdot)$$ n/a 15268 22
8033.2.bm $$\chi_{8033}(88, \cdot)$$ n/a 28512 44
8033.2.bn $$\chi_{8033}(95, \cdot)$$ n/a 16632 24
8033.2.bs $$\chi_{8033}(182, \cdot)$$ n/a 16632 24
8033.2.bt $$\chi_{8033}(104, \cdot)$$ n/a 30492 44
8033.2.by $$\chi_{8033}(331, \cdot)$$ n/a 30492 44
8033.2.bz $$\chi_{8033}(86, \cdot)$$ n/a 30448 44
8033.2.ca $$\chi_{8033}(28, \cdot)$$ n/a 30536 44
8033.2.cb $$\chi_{8033}(407, \cdot)$$ n/a 28512 44
8033.2.cc $$\chi_{8033}(16, \cdot)$$ n/a 91344 132
8033.2.cd $$\chi_{8033}(17, \cdot)$$ n/a 60984 88
8033.2.ci $$\chi_{8033}(99, \cdot)$$ n/a 60984 88
8033.2.cj $$\chi_{8033}(236, \cdot)$$ n/a 91608 132
8033.2.ck $$\chi_{8033}(74, \cdot)$$ n/a 91608 132
8033.2.cl $$\chi_{8033}(4, \cdot)$$ n/a 91344 132
8033.2.cm $$\chi_{8033}(23, \cdot)$$ n/a 182688 264
8033.2.cn $$\chi_{8033}(37, \cdot)$$ n/a 182952 264
8033.2.cs $$\chi_{8033}(2, \cdot)$$ n/a 182952 264
8033.2.ct $$\chi_{8033}(7, \cdot)$$ n/a 183216 264
8033.2.cu $$\chi_{8033}(9, \cdot)$$ n/a 183216 264
8033.2.cv $$\chi_{8033}(22, \cdot)$$ n/a 182688 264
8033.2.cw $$\chi_{8033}(14, \cdot)$$ n/a 365904 528
8033.2.db $$\chi_{8033}(11, \cdot)$$ n/a 365904 528

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8033))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8033)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(277))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

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