Space of modular forms of level 600, weight 1, and Character 600.bj

• Label: 600.1.bj
• Level: $600$
• Weight: $1$
• Character orbit: 600.bj
• Rep. character: $\chi_{600}(221,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	600.bj (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 600 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(600, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	8	8	0
Eisenstein series	16	16	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 2 q^{4} - 2 q^{6} - 4 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(600, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
600.1.bj.a	$600$	$1$	600.bj	600.aj	$10$	$4$	$1$	$0.299$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None		$4$	$0$	\(-1\)	\(-1\)	\(-1\)	\(-2\)	$1$		\(q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}q^{5}+\cdots\)
600.1.bj.b	$600$	$1$	600.bj	600.aj	$10$	$4$	$1$	$0.299$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None		$4$	$0$	\(1\)	\(1\)	\(1\)	\(-2\)	$1$		\(q+\zeta_{10}q^{2}-\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}q^{5}+\cdots\)