# Properties

 Label 2008.1.bd Level 2008 Weight 1 Character orbit bd Rep. character $$\chi_{2008}(3,\cdot)$$ Character field $$\Q(\zeta_{250})$$ Dimension 100 Newform subspaces 1 Sturm bound 252 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2008 = 2^{3} \cdot 251$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2008.bd (of order $$250$$ and degree $$100$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2008$$ Character field: $$\Q(\zeta_{250})$$ Newform subspaces: $$1$$ Sturm bound: $$252$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2008, [\chi])$$.

Total New Old
Modular forms 300 300 0
Cusp forms 100 100 0
Eisenstein series 200 200 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 100 0 0 0

## Trace form

 $$100q + O(q^{10})$$ $$100q - 25q^{22} - 25q^{32} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2008, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2008.1.bd.a $$100$$ $$1.002$$ $$\Q(\zeta_{250})$$ $$D_{125}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{250}^{35}q^{2}+(\zeta_{250}^{14}-\zeta_{250}^{53})q^{3}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5}$$
$3$ $$( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2}$$
$5$ $$( 1 - T^{5} + T^{10} - T^{15} + T^{20} )^{5}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5}$$
$7$ $$( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$11$ $$( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5}( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$13$ $$( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$17$ $$( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2}$$
$19$ $$( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2}$$
$23$ $$( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$29$ $$( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$31$ $$( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$37$ $$( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$41$ $$( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2}$$
$43$ $$( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2}$$
$47$ $$( 1 - T^{5} + T^{10} - T^{15} + T^{20} )^{5}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5}$$
$53$ $$( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$59$ $$( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5}( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$61$ $$( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$67$ $$( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2}$$
$71$ $$( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$73$ $$( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2}$$
$79$ $$( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$83$ $$( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5}( 1 + T^{25} + T^{50} + T^{75} + T^{100} )$$
$89$ $$( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2}$$
$97$ $$( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2}$$