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

• Label: 837.2.h
• Level: $837$
• Weight: $2$
• Character orbit: 837.h
• Rep. character: $\chi_{837}(676,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $86$
• Newform subspaces: $5$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

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

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

\( 86 q + 92 q^{4} + 3 q^{7} + O(q^{10}) \)

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.h.a	$837$	$2$	837.h	31.c	$3$	$2$	$1$	$6.683$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q-2q^{4}+(-5+5\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\cdots\)
837.2.h.b	$837$	$2$	837.h	31.c	$3$	$16$	$8$	$6.683$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{6}q^{2}+(1-\beta _{3})q^{4}-\beta _{8}q^{5}-\beta _{12}q^{7}+\cdots\)
837.2.h.c	$837$	$2$	837.h	31.c	$3$	$22$	$11$	$6.683$		None		$2$	$0$	\(-6\)	\(0\)	\(2\)	\(4\)		$\mathrm{SU}(2)[C_{3}]$
837.2.h.d	$837$	$2$	837.h	31.c	$3$	$22$	$11$	$6.683$		None		$2$	$0$	\(6\)	\(0\)	\(-2\)	\(4\)		$\mathrm{SU}(2)[C_{3}]$
837.2.h.e	$837$	$2$	837.h	31.c	$3$	$24$	$12$	$6.683$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(837, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 2}\)