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

• Label: 237.2.i
• Level: $237$
• Weight: $2$
• Character orbit: 237.i
• Rep. character: $\chi_{237}(10,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $168$
• Newform subspaces: $2$
• Sturm bound: $53$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 237 = 3 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	237.i (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{13})\)
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	336	168	168
Cusp forms	288	168	120
Eisenstein series	48	0	48

Trace form

\( 168 q - 4 q^{2} - 2 q^{3} - 24 q^{4} - 6 q^{6} - 12 q^{7} + 40 q^{8} - 14 q^{9} + O(q^{10}) \)

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.i.a	$237$	$2$	237.i	79.e	$13$	$72$	$6$	$1.892$		None		$2$	$0$	\(1\)	\(6\)	\(-9\)	\(0\)		$\mathrm{SU}(2)[C_{13}]$
237.2.i.b	$237$	$2$	237.i	79.e	$13$	$96$	$8$	$1.892$		None		$2$	$0$	\(-5\)	\(-8\)	\(9\)	\(-12\)		$\mathrm{SU}(2)[C_{13}]$

Decomposition of \(S_{2}^{\mathrm{old}}(237, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(237, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 2}\)