# Properties

 Label 2008.1.c Level 2008 Weight 1 Character orbit c Rep. character $$\chi_{2008}(501,\cdot)$$ Character field $$\Q$$ Dimension 6 Newform subspaces 2 Sturm bound 252 Trace bound 2

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6q + 6q^{4} - 2q^{7} + 6q^{9} + O(q^{10})$$ $$6q + 6q^{4} - 2q^{7} + 6q^{9} + 6q^{16} - 2q^{17} - 2q^{22} - 2q^{23} + 6q^{25} - 2q^{28} - 2q^{31} + 6q^{36} - 2q^{38} - 2q^{41} + 4q^{49} - 2q^{58} - 2q^{63} + 6q^{64} - 2q^{68} - 2q^{73} - 2q^{74} - 2q^{79} + 6q^{81} - 2q^{86} - 2q^{88} - 2q^{89} - 2q^{92} + O(q^{100})$$

## 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.c.a $$3$$ $$1.002$$ $$\Q(\zeta_{14})^+$$ $$D_{7}$$ $$\Q(\sqrt{-502})$$ None $$-3$$ $$0$$ $$0$$ $$-1$$ $$q-q^{2}+q^{4}-\beta _{1}q^{7}-q^{8}+q^{9}-\beta _{2}q^{11}+\cdots$$
2008.1.c.b $$3$$ $$1.002$$ $$\Q(\zeta_{14})^+$$ $$D_{7}$$ $$\Q(\sqrt{-502})$$ None $$3$$ $$0$$ $$0$$ $$-1$$ $$q+q^{2}+q^{4}-\beta _{1}q^{7}+q^{8}+q^{9}+\beta _{2}q^{11}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 + T )^{3}$$)($$( 1 - T )^{3}$$)
$3$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$5$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$7$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$11$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$13$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$17$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$19$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$23$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$29$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$31$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$37$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$41$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$43$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$47$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$53$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$59$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$61$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$67$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$71$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$73$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$79$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$83$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$89$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$97$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)