Space of modular forms of level 576, weight 1, and Character 576.b

• Label: 576.1.b
• Level: $576$
• Weight: $1$
• Character orbit: 576.b
• Rep. character: $\chi_{576}(415,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	576.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(576, [\chi])\).

	Total	New	Old
Modular forms	26	2	24
Cusp forms	2	2	0
Eisenstein series	24	0	24

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

\( 2 q + 2 q^{25} - 6 q^{49} - 4 q^{73} + 4 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
576.1.b.a	$576$	$1$	576.b	8.d	$2$	$2$	$2$	$0.287$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{2}) \)		✓	✓	✓	576.1.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q-2 i q^{7}+q^{25}+2 i q^{31}-3 q^{49}+\cdots\)