Space of modular forms of level 1008, weight 1, and Character 1008.f

• Label: 1008.1.f
• Level: $1008$
• Weight: $1$
• Character orbit: 1008.f
• Rep. character: $\chi_{1008}(433,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1008.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1008, [\chi])\).

	Total	New	Old
Modular forms	30	2	28
Cusp forms	6	1	5
Eisenstein series	24	1	23

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

\( q + q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1008, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1008.1.f.a	$1008$	$1$	1008.f	7.b	$2$	$1$	$1$	$0.503$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{21}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+q^{7}+q^{25}-2q^{37}+2q^{43}+q^{49}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)