Space of modular forms of level 1004, weight 1, and Character 1004.d

• Label: 1004.1.d
• Level: $1004$
• Weight: $1$
• Character orbit: 1004.d
• Rep. character: $\chi_{1004}(501,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $2$
• Sturm bound: $126$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1004 = 2^{2} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1004.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 251 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(126\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1004, [\chi])\).

	Total	New	Old
Modular forms	19	7	12
Cusp forms	16	7	9
Eisenstein series	3	0	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	7	0	0	0

Trace form

\( 7 q + 7 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1004, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1004.1.d.a	$1004$	$1$	1004.d	251.b	$2$	$1$	$1$	$0.501$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-251}) \)	None	✓	$2$	$0$	\(0\)	\(2\)	\(-1\)	\(-1\)	$1$		\(q+2q^{3}-q^{5}-q^{7}+3q^{9}+2q^{13}+\cdots\)
1004.1.d.b	$1004$	$1$	1004.d	251.b	$2$	$6$	$6$	$0.501$	\(\Q(\zeta_{21})^+\)	$D_{21}$	\(\Q(\sqrt{-251}) \)	None	✓	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(1\)	$1$		\(q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1004, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1004, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(251, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(502, [\chi])\)\(^{\oplus 2}\)