Space of modular forms of level 237, weight 4, and Character 237.e

• Label: 237.4.e
• Level: $237$
• Weight: $4$
• Character orbit: 237.e
• Rep. character: $\chi_{237}(55,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $106$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 237 = 3 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(106\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(237, [\chi])\).

	Total	New	Old
Modular forms	164	80	84
Cusp forms	156	80	76
Eisenstein series	8	0	8

Trace form

80 * q - 2 * q^2 + 6 * q^3 - 138 * q^4 + 2 * q^7 + 168 * q^8 - 360 * q^9 - 48 * q^10 + 60 * q^11 - 120 * q^12 - 34 * q^13 - 140 * q^14 - 204 * q^15 - 590 * q^16 - 32 * q^17 + 36 * q^18 - 164 * q^19 + 190 * q^20 + 216 * q^21 + 464 * q^22 + 128 * q^23 - 180 * q^24 - 998 * q^25 - 240 * q^26 - 108 * q^27 - 172 * q^28 + 384 * q^29 + 324 * q^30 + 188 * q^31 - 114 * q^32 - 300 * q^33 + 904 * q^34 + 48 * q^35 - 1242 * q^36 + 570 * q^37 - 1328 * q^38 + 174 * q^39 + 214 * q^40 + 72 * q^41 + 180 * q^42 - 430 * q^43 - 252 * q^44 - 3880 * q^46 - 456 * q^47 + 576 * q^48 - 502 * q^49 - 1830 * q^50 + 708 * q^51 + 688 * q^52 - 1804 * q^53 + 66 * q^55 + 2522 * q^56 - 2064 * q^57 - 1312 * q^58 + 1148 * q^59 + 324 * q^60 - 792 * q^61 + 1780 * q^62 + 18 * q^63 + 5728 * q^64 + 2104 * q^65 + 1356 * q^66 + 1260 * q^67 - 208 * q^68 + 1056 * q^69 - 3262 * q^70 + 3680 * q^71 - 756 * q^72 - 12 * q^73 + 2792 * q^74 + 1986 * q^75 - 4508 * q^76 + 1536 * q^77 - 2712 * q^78 + 4082 * q^79 + 6196 * q^80 - 3240 * q^81 - 5770 * q^82 + 1036 * q^83 - 1008 * q^84 + 1544 * q^85 - 1114 * q^86 - 588 * q^87 - 1904 * q^88 - 2832 * q^89 + 216 * q^90 - 3304 * q^91 - 2184 * q^92 - 636 * q^93 + 3396 * q^94 + 2956 * q^95 - 1380 * q^96 + 2776 * q^97 - 6318 * q^98 + 540 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(237, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
237.4.e.a	$237$	$4$	237.e	79.c	$3$	$38$	$19$	$13.983$		None		✓			237.4.e.a	$2$	$0$	\(-1\)	\(-57\)	\(17\)	\(-17\)		$\mathrm{SU}(2)[C_{3}]$
237.4.e.b	$237$	$4$	237.e	79.c	$3$	$42$	$21$	$13.983$		None		✓	✓		237.4.e.b	$2$	$0$	\(-1\)	\(63\)	\(-17\)	\(19\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{4}^{\mathrm{old}}(237, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(237, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 2}\)