# Properties

 Label 2003.1 Level 2003 Weight 1 Dimension 4 Nonzero newspaces 1 Newform subspaces 2 Sturm bound 334334 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$2003$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$2$$ Sturm bound: $$334334$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2003))$$.

Total New Old
Modular forms 1005 1005 0
Cusp forms 4 4 0
Eisenstein series 1001 1001 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4q - q^{3} + 4q^{4} + 3q^{9} + O(q^{10})$$ $$4q - q^{3} + 4q^{4} + 3q^{9} - q^{12} - q^{13} + 4q^{16} - q^{19} + 4q^{25} - 2q^{27} + 3q^{36} - 2q^{39} - q^{47} - q^{48} + 4q^{49} - q^{52} - q^{53} - 2q^{57} - q^{59} + 4q^{64} - q^{73} - q^{75} - q^{76} - q^{79} + 2q^{81} - q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2003))$$

We only show spaces with odd 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
2003.1.b $$\chi_{2003}(2002, \cdot)$$ 2003.1.b.a 1 1
2003.1.b.b 3
2003.1.f $$\chi_{2003}(318, \cdot)$$ None 0 6
2003.1.g $$\chi_{2003}(180, \cdot)$$ None 0 10
2003.1.h $$\chi_{2003}(45, \cdot)$$ None 0 12
2003.1.l $$\chi_{2003}(50, \cdot)$$ None 0 60
2003.1.m $$\chi_{2003}(6, \cdot)$$ None 0 72
2003.1.n $$\chi_{2003}(2, \cdot)$$ None 0 120
2003.1.p $$\chi_{2003}(5, \cdot)$$ None 0 720

## Hecke Characteristic Polynomials

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