Space of modular forms of level 2008, weight 1, and Character 2008.bd

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

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

\( 100 q + O(q^{10}) \)

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2008.1.bd.a	$2008$	$1$	2008.bd	2008.ad	$250$	$100$	$1$	$1.002$	\(\Q(\zeta_{250})\)	$D_{125}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{250}^{35}q^{2}+(\zeta_{250}^{14}-\zeta_{250}^{53})q^{3}+\cdots\)