# Properties

 Label 4003.2 Level 4003 Weight 2 Dimension 665667 Nonzero newspaces 8 Sturm bound 2.67067e+06

## Defining parameters

 Level: $$N$$ = $$4003\( 4003$$ \) Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$2670668$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4003))$$.

Total New Old
Modular forms 669668 669668 0
Cusp forms 665667 665667 0
Eisenstein series 4001 4001 0

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4003))$$

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
4003.2.a $$\chi_{4003}(1, \cdot)$$ 4003.2.a.a 2 1
4003.2.a.b 152
4003.2.a.c 179
4003.2.c $$\chi_{4003}(822, \cdot)$$ n/a 666 2
4003.2.e $$\chi_{4003}(551, \cdot)$$ n/a 7304 22
4003.2.f $$\chi_{4003}(102, \cdot)$$ n/a 9296 28
4003.2.i $$\chi_{4003}(129, \cdot)$$ n/a 14652 44
4003.2.j $$\chi_{4003}(10, \cdot)$$ n/a 18648 56
4003.2.m $$\chi_{4003}(6, \cdot)$$ n/a 204512 616
4003.2.o $$\chi_{4003}(4, \cdot)$$ n/a 410256 1232

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

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T^{2} + 4 T^{4}$$)
$3$ ($$1 + 4 T^{2} + 9 T^{4}$$)
$5$ ($$1 + 8 T^{2} + 25 T^{4}$$)
$7$ ($$( 1 + T + 7 T^{2} )^{2}$$)
$11$ ($$1 + 4 T + 18 T^{2} + 44 T^{3} + 121 T^{4}$$)
$13$ ($$1 - 8 T + 34 T^{2} - 104 T^{3} + 169 T^{4}$$)
$17$ ($$1 + 2 T + 3 T^{2} + 34 T^{3} + 289 T^{4}$$)
$19$ ($$1 - 2 T + 7 T^{2} - 38 T^{3} + 361 T^{4}$$)
$23$ ($$1 + 12 T + 74 T^{2} + 276 T^{3} + 529 T^{4}$$)
$29$ ($$1 + 8 T + 66 T^{2} + 232 T^{3} + 841 T^{4}$$)
$31$ ($$1 - 4 T - 6 T^{2} - 124 T^{3} + 961 T^{4}$$)
$37$ ($$1 + 14 T + 115 T^{2} + 518 T^{3} + 1369 T^{4}$$)
$41$ ($$1 - 16 T + 138 T^{2} - 656 T^{3} + 1681 T^{4}$$)
$43$ ($$( 1 + 43 T^{2} )^{2}$$)
$47$ ($$1 - 8 T + 60 T^{2} - 376 T^{3} + 2209 T^{4}$$)
$53$ ($$1 + 4 T - 18 T^{2} + 212 T^{3} + 2809 T^{4}$$)
$59$ ($$1 + 12 T + 146 T^{2} + 708 T^{3} + 3481 T^{4}$$)
$61$ ($$1 - 20 T + 214 T^{2} - 1220 T^{3} + 3721 T^{4}$$)
$67$ ($$1 - 14 T + 151 T^{2} - 938 T^{3} + 4489 T^{4}$$)
$71$ ($$( 1 - 6 T + 71 T^{2} )^{2}$$)
$73$ ($$( 1 + 3 T + 73 T^{2} )^{2}$$)
$79$ ($$1 - 6 T + 95 T^{2} - 474 T^{3} + 6241 T^{4}$$)
$83$ ($$1 - 6 T - 25 T^{2} - 498 T^{3} + 6889 T^{4}$$)
$89$ ($$1 + 18 T + 251 T^{2} + 1602 T^{3} + 7921 T^{4}$$)
$97$ ($$1 - 12 T + 212 T^{2} - 1164 T^{3} + 9409 T^{4}$$)