Space of modular forms of level 237, weight 2, and Character 237.n

• Label: 237.2.n
• Level: $237$
• Weight: $2$
• Character orbit: 237.n
• Rep. character: $\chi_{237}(29,\cdot)$
• Character field: $\Q(\zeta_{78})$
• Dimension: $600$
• Newform subspaces: $2$
• Sturm bound: $53$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 237 = 3 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	237.n (of order \(78\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 237 \)
Character field:			\(\Q(\zeta_{78})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(53\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(237, [\chi])\).

	Total	New	Old
Modular forms	696	696	0
Cusp forms	600	600	0
Eisenstein series	96	96	0

Trace form

\( 600 q - 23 q^{3} - 70 q^{4} - 23 q^{6} - 34 q^{7} - 27 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(237, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
237.2.n.a	$237$	$2$	237.n	237.n	$78$	$24$	$1$	$1.892$		\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(3\)	\(0\)	\(6\)		$\mathrm{U}(1)[D_{78}]$
237.2.n.b	$237$	$2$	237.n	237.n	$78$	$576$	$24$	$1.892$		None		$4$	$0$	\(0\)	\(-26\)	\(0\)	\(-40\)		$\mathrm{SU}(2)[C_{78}]$