Space of modular forms of level 468, weight 1, and Character 468.cd

• Label: 468.1.cd
• Level: $468$
• Weight: $1$
• Character orbit: 468.cd
• Rep. character: $\chi_{468}(37,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	468.cd (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(468, [\chi])\).

	Total	New	Old
Modular forms	52	4	48
Cusp forms	4	4	0
Eisenstein series	48	0	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 2 q^{7} + 2 q^{19} - 2 q^{31} - 2 q^{37} - 6 q^{43} - 6 q^{49} - 4 q^{67} + 2 q^{73} + 2 q^{91} - 2 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(468, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
468.1.cd.a	$468$	$1$	468.cd	13.f	$12$	$4$	$1$	$0.234$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	468.1.cd.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{7}-\zeta_{12}q^{13}+(\zeta_{12}+\cdots)q^{19}+\cdots\)