Space of modular forms of level 1836, weight 1, and Character 1836.j

• Label: 1836.1.j
• Level: $1836$
• Weight: $1$
• Character orbit: 1836.j
• Rep. character: $\chi_{1836}(701,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $324$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1836 = 2^{2} \cdot 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1836.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 51 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(324\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1836, [\chi])\).

	Total	New	Old
Modular forms	48	4	44
Cusp forms	12	4	8
Eisenstein series	36	0	36

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

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

Trace form

\( 4 q + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1836, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1836.1.j.a	$1836$	$1$	1836.j	51.f	$4$	$4$	$2$	$0.916$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		✓	✓	✓	1836.1.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q+\zeta_{8}q^{5}+(1+\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1836, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1836, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 2}\)