Space of modular forms of level 52, weight 1, and Character 52.j

• Label: 52.1.j
• Level: $52$
• Weight: $1$
• Character orbit: 52.j
• Rep. character: $\chi_{52}(3,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $7$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	52.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(7\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(52, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

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 - q^2 - q^4 - 2 * q^5 + 2 * q^8 - q^9 + q^10 - q^13 - q^16 + q^17 + 2 * q^18 + q^20 - q^26 + q^29 - q^32 - 2 * q^34 - q^36 + q^37 - 2 * q^40 + q^41 + q^45 - q^49 + 2 * q^52 - 2 * q^53 + q^58 + q^61 + 2 * q^64 + q^65 + q^68 - q^72 - 2 * q^73 + q^74 + q^80 - q^81 + q^82 - q^85 - 2 * q^89 - 2 * q^90 - 2 * q^97 - q^98

Decomposition of \(S_{1}^{\mathrm{new}}(52, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
52.1.j.a	$52$	$1$	52.j	52.j	$6$	$2$	$1$	$0.026$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	52.1.j.a	$4$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)