# Properties

 Label 8003.2 Level 8003 Weight 2 Dimension 2.65786e+06 Nonzero newspaces 36 Sturm bound 1.06704e+07

## Defining parameters

 Level: $$N$$ = $$8003 = 53 \cdot 151$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$10670400$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8003))$$.

Total New Old
Modular forms 2675400 2673065 2335
Cusp forms 2659801 2657865 1936
Eisenstein series 15599 15200 399

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8003))$$

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
8003.2.a $$\chi_{8003}(1, \cdot)$$ 8003.2.a.a 147 1
8003.2.a.b 153
8003.2.a.c 172
8003.2.a.d 179
8003.2.b $$\chi_{8003}(6041, \cdot)$$ n/a 674 1
8003.2.e $$\chi_{8003}(1326, \cdot)$$ n/a 1316 2
8003.2.g $$\chi_{8003}(2415, \cdot)$$ n/a 1364 2
8003.2.h $$\chi_{8003}(5142, \cdot)$$ n/a 2640 4
8003.2.j $$\chi_{8003}(3656, \cdot)$$ n/a 1364 2
8003.2.m $$\chi_{8003}(3179, \cdot)$$ n/a 2728 4
8003.2.o $$\chi_{8003}(1090, \cdot)$$ n/a 2728 4
8003.2.q $$\chi_{8003}(152, \cdot)$$ n/a 8112 12
8003.2.r $$\chi_{8003}(1061, \cdot)$$ n/a 5264 8
8003.2.s $$\chi_{8003}(394, \cdot)$$ n/a 5456 8
8003.2.u $$\chi_{8003}(160, \cdot)$$ n/a 13200 20
8003.2.x $$\chi_{8003}(303, \cdot)$$ n/a 8088 12
8003.2.ba $$\chi_{8003}(105, \cdot)$$ n/a 5456 8
8003.2.bb $$\chi_{8003}(183, \cdot)$$ n/a 16368 24
8003.2.be $$\chi_{8003}(370, \cdot)$$ n/a 13640 20
8003.2.bf $$\chi_{8003}(603, \cdot)$$ n/a 16368 24
8003.2.bi $$\chi_{8003}(23, \cdot)$$ n/a 10912 16
8003.2.bj $$\chi_{8003}(819, \cdot)$$ n/a 32736 48
8003.2.bk $$\chi_{8003}(213, \cdot)$$ n/a 26320 40
8003.2.bm $$\chi_{8003}(269, \cdot)$$ n/a 16368 24
8003.2.bp $$\chi_{8003}(83, \cdot)$$ n/a 27280 40
8003.2.br $$\chi_{8003}(59, \cdot)$$ n/a 32736 48
8003.2.bt $$\chi_{8003}(423, \cdot)$$ n/a 27280 40
8003.2.bx $$\chi_{8003}(33, \cdot)$$ n/a 32736 48
8003.2.by $$\chi_{8003}(16, \cdot)$$ n/a 65472 96
8003.2.ca $$\chi_{8003}(87, \cdot)$$ n/a 65472 96
8003.2.cb $$\chi_{8003}(30, \cdot)$$ n/a 54560 80
8003.2.cd $$\chi_{8003}(44, \cdot)$$ n/a 163680 240
8003.2.ce $$\chi_{8003}(4, \cdot)$$ n/a 65472 96
8003.2.ci $$\chi_{8003}(9, \cdot)$$ n/a 163680 240
8003.2.ck $$\chi_{8003}(75, \cdot)$$ n/a 130944 192
8003.2.cm $$\chi_{8003}(10, \cdot)$$ n/a 327360 480
8003.2.cn $$\chi_{8003}(3, \cdot)$$ n/a 327360 480
8003.2.cq $$\chi_{8003}(11, \cdot)$$ n/a 327360 480
8003.2.ct $$\chi_{8003}(12, \cdot)$$ n/a 654720 960

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8003))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8003)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(53))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(151))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database