# Properties

 Label 2003.1.b Level 2003 Weight 1 Character orbit b Rep. character $$\chi_{2003}(2002,\cdot)$$ Character field $$\Q$$ Dimension 4 Newform subspaces 2 Sturm bound 167 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$2003$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 2003.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$2003$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$167$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2003, [\chi])$$.

Total New Old
Modular forms 5 5 0
Cusp forms 4 4 0
Eisenstein series 1 1 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 $$S_{1}^{\mathrm{new}}(2003, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2003.1.b.a $$1$$ $$1.000$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-2003})$$ None $$0$$ $$-1$$ $$0$$ $$0$$ $$q-q^{3}+q^{4}-q^{12}-q^{13}+q^{16}+2q^{19}+\cdots$$
2003.1.b.b $$3$$ $$1.000$$ $$\Q(\zeta_{18})^+$$ $$D_{9}$$ $$\Q(\sqrt{-2003})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}-\beta _{1}q^{12}+\cdots$$

## Hecke Characteristic Polynomials

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