Space of modular forms of level 837, weight 2, and Character 837.j

• Label: 837.2.j
• Level: $837$
• Weight: $2$
• Character orbit: 837.j
• Rep. character: $\chi_{837}(26,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $86$
• Newform subspaces: $6$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 837 = 3^{3} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	837.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 93 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(837, [\chi])\).

	Total	New	Old
Modular forms	204	86	118
Cusp forms	180	86	94
Eisenstein series	24	0	24

Trace form

\( 86 q - 92 q^{4} + 7 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(837, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
837.2.j.a	$837$	$2$	837.j	93.g	$6$	$2$	$1$	$6.683$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{2}-q^{4}+(-4+2\zeta_{6})q^{5}+\cdots\)
837.2.j.b	$837$	$2$	837.j	93.g	$6$	$2$	$1$	$6.683$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{2}-q^{4}+(4-2\zeta_{6})q^{5}+\cdots\)
837.2.j.c	$837$	$2$	837.j	93.g	$6$	$2$	$1$	$6.683$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+2q^{4}+(-5+5\zeta_{6})q^{7}+(6-3\zeta_{6})q^{13}+\cdots\)
837.2.j.d	$837$	$2$	837.j	93.g	$6$	$16$	$8$	$6.683$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{2}+(-2-\beta _{1}+\beta _{7})q^{4}-\beta _{3}q^{5}+\cdots\)
837.2.j.e	$837$	$2$	837.j	93.g	$6$	$20$	$10$	$6.683$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{11}+\beta _{15})q^{2}+(-1+\beta _{9}+\beta _{13}+\cdots)q^{4}+\cdots\)
837.2.j.f	$837$	$2$	837.j	93.g	$6$	$44$	$22$	$6.683$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(837, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(837, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 2}\)