Space of modular forms of level 187, weight 4, and Character 187.g

• Label: 187.4.g
• Level: $187$
• Weight: $4$
• Character orbit: 187.g
• Rep. character: $\chi_{187}(69,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $192$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(187, [\chi])\).

	Total	New	Old
Modular forms	224	192	32
Cusp forms	208	192	16
Eisenstein series	16	0	16

Trace form

192 * q + 4 * q^2 + 4 * q^3 - 212 * q^4 - 8 * q^5 + 24 * q^6 + 52 * q^7 - 116 * q^8 - 464 * q^9 - 64 * q^10 + 8 * q^11 - 208 * q^12 + 48 * q^13 + 234 * q^14 + 200 * q^15 - 12 * q^16 + 68 * q^17 - 158 * q^18 - 160 * q^19 - 698 * q^20 + 40 * q^21 - 402 * q^22 - 168 * q^23 + 1024 * q^24 - 408 * q^25 + 370 * q^26 + 124 * q^27 + 422 * q^28 + 388 * q^29 + 448 * q^30 + 844 * q^31 + 796 * q^32 - 1284 * q^33 - 892 * q^35 - 1816 * q^36 + 240 * q^37 + 404 * q^38 + 1084 * q^39 + 380 * q^40 - 484 * q^41 + 770 * q^42 + 1304 * q^43 - 2304 * q^44 - 1032 * q^45 - 3470 * q^46 - 580 * q^47 - 1474 * q^48 - 3964 * q^49 - 1088 * q^50 + 408 * q^51 + 1656 * q^52 + 1120 * q^53 + 7204 * q^54 + 464 * q^55 + 3516 * q^56 + 1144 * q^57 - 1346 * q^58 - 1020 * q^59 - 5476 * q^60 - 348 * q^61 - 544 * q^62 - 1108 * q^63 + 1168 * q^64 - 2840 * q^65 + 1928 * q^66 + 4648 * q^67 + 816 * q^68 - 1788 * q^69 + 84 * q^70 + 1036 * q^71 + 1858 * q^72 + 3548 * q^73 - 2028 * q^74 - 656 * q^75 - 1348 * q^76 + 5280 * q^77 + 10424 * q^78 + 8 * q^79 + 8720 * q^80 - 4476 * q^81 - 836 * q^82 - 652 * q^83 - 6460 * q^84 - 476 * q^85 - 5924 * q^86 + 2432 * q^87 - 13790 * q^88 - 6464 * q^89 - 4496 * q^90 + 10248 * q^91 + 1950 * q^92 + 4536 * q^93 - 448 * q^94 - 964 * q^95 - 7088 * q^96 + 7632 * q^97 - 4616 * q^98 + 7440 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(187, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
187.4.g.a	$187$	$4$	187.g	11.c	$5$	$88$	$22$	$11.033$		None		✓			187.4.g.a	$2$	$0$	\(2\)	\(14\)	\(42\)	\(16\)		$\mathrm{SU}(2)[C_{5}]$
187.4.g.b	$187$	$4$	187.g	11.c	$5$	$104$	$26$	$11.033$		None		✓	✓		187.4.g.b	$2$	$0$	\(2\)	\(-10\)	\(-50\)	\(36\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{4}^{\mathrm{old}}(187, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(187, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)