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

• Label: 600.1.n
• Level: $600$
• Weight: $1$
• Character orbit: 600.n
• Rep. character: $\chi_{600}(101,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• 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.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
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	14	8	6
Cusp forms	2	2	0
Eisenstein series	12	6	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

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

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.n.a	$600$	$1$	600.n	24.h	$2$	$1$	$1$	$0.299$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{10}) \)	✓	$4$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
600.1.n.b	$600$	$1$	600.n	24.h	$2$	$1$	$1$	$0.299$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{10}) \)	✓	$4$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)