Space of modular forms of level 127, weight 4, and Character 127.i

• Label: 127.4.i
• Level: $127$
• Weight: $4$
• Character orbit: 127.i
• Rep. character: $\chi_{127}(25,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $372$
• Newform subspaces: $1$
• Sturm bound: $42$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 127 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	127.i (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 127 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(42\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(127, [\chi])\).

	Total	New	Old
Modular forms	396	396	0
Cusp forms	372	372	0
Eisenstein series	24	24	0

Trace form

372 * q - 15 * q^2 - 13 * q^3 - 225 * q^4 - 30 * q^5 - 105 * q^6 + 45 * q^7 - 138 * q^8 + 318 * q^9 + 30 * q^10 - 83 * q^11 - 23 * q^12 + 41 * q^13 - 408 * q^14 - 168 * q^15 - 1129 * q^16 - 45 * q^17 + 353 * q^18 + 264 * q^19 + 1664 * q^20 + 1507 * q^21 - 29 * q^22 - 97 * q^23 - 979 * q^24 - 1076 * q^25 - 1324 * q^26 - 52 * q^27 - 461 * q^28 + 349 * q^29 + 653 * q^30 - 43 * q^31 + 1665 * q^32 - 448 * q^33 - 3500 * q^34 - 2228 * q^35 + 3280 * q^36 + 272 * q^37 - 1491 * q^38 + 5541 * q^39 - 1186 * q^40 + 593 * q^41 - 788 * q^42 + 21 * q^43 - 2712 * q^44 - 40 * q^45 - 3549 * q^46 - 124 * q^47 + 4002 * q^48 - 274 * q^49 + 1956 * q^50 + 10 * q^51 + 3294 * q^52 + 745 * q^53 + 816 * q^54 + 1220 * q^55 + 6658 * q^56 - 1000 * q^57 + 3114 * q^58 - 3756 * q^59 + 1400 * q^60 + 1238 * q^61 - 13157 * q^62 - 2534 * q^63 - 3122 * q^64 - 4420 * q^65 - 410 * q^66 - 4065 * q^67 + 1584 * q^68 + 131 * q^69 + 1011 * q^70 + 7181 * q^71 + 6423 * q^72 - 1140 * q^73 - 3271 * q^74 + 2386 * q^75 - 2139 * q^76 - 1092 * q^77 - 2393 * q^78 + 4105 * q^79 + 12638 * q^80 + 3039 * q^81 - 6532 * q^82 - 313 * q^83 - 15676 * q^84 + 1372 * q^85 + 4343 * q^86 - 8840 * q^87 + 28158 * q^88 - 314 * q^89 - 5563 * q^90 + 3531 * q^91 - 4923 * q^92 - 7341 * q^93 - 92 * q^94 + 1092 * q^95 + 9237 * q^96 - 2911 * q^97 - 5859 * q^98 + 143 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(127, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
127.4.i.a	$127$	$4$	127.i	127.i	$21$	$372$	$31$	$7.493$		None		✓	✓	✓	127.4.i.a	$2$	$0$	\(-15\)	\(-13\)	\(-30\)	\(45\)		$\mathrm{SU}(2)[C_{21}]$