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

• Label: 237.2.e
• Level: $237$
• Weight: $2$
• Character orbit: 237.e
• Rep. character: $\chi_{237}(55,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $26$
• Newform subspaces: $2$
• Sturm bound: $53$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 237 = 3 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	237.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{3})\)
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	58	26	32
Cusp forms	50	26	24
Eisenstein series	8	0	8

Trace form

\( 26 q + 2 q^{2} - q^{3} - 14 q^{4} - 6 q^{6} - 4 q^{7} - 13 q^{9} + O(q^{10}) \)

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.e.a	$237$	$2$	237.e	79.c	$3$	$12$	$6$	$1.892$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(4\)	\(6\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}+\beta _{4})q^{2}+(1+\beta _{4})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
237.2.e.b	$237$	$2$	237.e	79.c	$3$	$14$	$7$	$1.892$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-7\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{7})q^{3}+(-\beta _{4}-\beta _{7}+\cdots)q^{4}+\cdots\)

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

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