# Properties

 Label 2008.1.j Level 2008 Weight 1 Character orbit j Rep. character $$\chi_{2008}(219,\cdot)$$ Character field $$\Q(\zeta_{10})$$ Dimension 4 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.j (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2008$$ Character field: $$\Q(\zeta_{10})$$ 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 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 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

 $$4q + 4q^{2} - 2q^{3} + 4q^{4} - 2q^{6} + 4q^{8} - 3q^{9} + O(q^{10})$$ $$4q + 4q^{2} - 2q^{3} + 4q^{4} - 2q^{6} + 4q^{8} - 3q^{9} + 3q^{11} - 2q^{12} + 4q^{16} - 2q^{17} - 3q^{18} - 2q^{19} + 3q^{22} - 2q^{24} + 4q^{25} + q^{27} + 4q^{32} + q^{33} - 2q^{34} - 3q^{36} - 2q^{38} - 2q^{41} - 2q^{43} + 3q^{44} - 2q^{48} - q^{49} + 4q^{50} - 4q^{51} + q^{54} - 4q^{57} + 3q^{59} + 4q^{64} + q^{66} - 2q^{67} - 2q^{68} - 3q^{72} - 2q^{73} - 2q^{75} - 2q^{76} - 2q^{82} + 3q^{83} - 2q^{86} + 3q^{88} - 2q^{89} - 2q^{96} - 2q^{97} - q^{98} - q^{99} + O(q^{100})$$

## 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.j.a $$4$$ $$1.002$$ $$\Q(\zeta_{10})$$ $$D_{5}$$ $$\Q(\sqrt{-2})$$ None $$4$$ $$-2$$ $$0$$ $$0$$ $$q+q^{2}+(-\zeta_{10}+\zeta_{10}^{2})q^{3}+q^{4}+(-\zeta_{10}+\cdots)q^{6}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$( 1 - T )^{4}$$
$3$ $$( 1 + T + T^{2} + T^{3} + T^{4} )^{2}$$
$5$ $$( 1 - T )^{4}( 1 + T )^{4}$$
$7$ $$( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} )$$
$11$ $$( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )$$
$13$ $$( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} )$$
$17$ $$( 1 + T + T^{2} + T^{3} + T^{4} )^{2}$$
$19$ $$( 1 + T + T^{2} + T^{3} + T^{4} )^{2}$$
$23$ $$( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} )$$
$29$ $$( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} )$$
$31$ $$( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} )$$
$37$ $$( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} )$$
$41$ $$( 1 + T + T^{2} + T^{3} + T^{4} )^{2}$$
$43$ $$( 1 + T + T^{2} + T^{3} + T^{4} )^{2}$$
$47$ $$( 1 - T )^{4}( 1 + T )^{4}$$
$53$ $$( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} )$$
$59$ $$( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )$$
$61$ $$( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} )$$
$67$ $$( 1 + T + T^{2} + T^{3} + T^{4} )^{2}$$
$71$ $$( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} )$$
$73$ $$( 1 + T + T^{2} + T^{3} + T^{4} )^{2}$$
$79$ $$( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} )$$
$83$ $$( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )$$
$89$ $$( 1 + T + T^{2} + T^{3} + T^{4} )^{2}$$
$97$ $$( 1 + T + T^{2} + T^{3} + T^{4} )^{2}$$