Space of modular forms of level 16, weight 28, and Character 16.e

• Label: 16.28.e
• Level: $16$
• Weight: $28$
• Character orbit: 16.e
• Rep. character: $\chi_{16}(5,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $106$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$16 = 2^{4}$
Weight:	$k$	$=$	$28$
Character orbit:	$[\chi]$	$=$	16.e (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$16$
Character field:			$\Q(i)$
Newform subspaces:			$1$
Sturm bound:			$56$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{28}(16, [\chi])$.

	Total	New	Old
Modular forms	110	110	0
Cusp forms	106	106	0
Eisenstein series	4	4	0

Trace form

106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8 + 8247210235372 * q^10 - 34039821810222 * q^11 + 1748989708884580 * q^12 - 2 * q^13 - 7155218316814660 * q^14 - 15569560546875004 * q^15 - 11277270898466024 * q^16 - 4 * q^17 - 142926567667036386 * q^18 - 361273435637780378 * q^19 + 442470438134323004 * q^20 + 15251194969972 * q^21 - 1169169681057307068 * q^22 + 10984755246449911984 * q^24 + 17037255844415508360 * q^26 - 16968259081125930056 * q^27 - 60190300783057535720 * q^28 - 27121773564864273802 * q^29 - 676957577616991436364 * q^30 + 293010555569340511088 * q^31 - 1166901104384201893432 * q^32 - 4 * q^33 - 290590654320714186380 * q^34 - 1483431258098321642404 * q^35 + 2272823118258680645548 * q^36 - 470486119578222882250 * q^37 - 7667804020978176078752 * q^38 - 13361029860556314821176 * q^40 - 46808273599641292573640 * q^42 + 30832447383975033909242 * q^43 + 78151525061974584923236 * q^44 + 14901145942652686274 * q^45 - 30741189488837489213204 * q^46 - 109219994122411663546544 * q^47 - 189351174993879449193752 * q^48 - 882423151738888904731010 * q^49 + 548328807383867462419206 * q^50 - 115559869623218432212572 * q^51 - 870962460180776269413356 * q^52 - 5971340109916911897018 * q^53 + 1136059014139929162305056 * q^54 + 1200724087407057566405656 * q^56 - 2828993593282901350448872 * q^58 - 34394779779101149275670 * q^59 + 7255680995179605171006528 * q^60 - 2475467954128860415560434 * q^61 - 3746979776437258967395280 * q^62 + 5188426743337460248956228 * q^63 - 998638142638832585325568 * q^64 + 2911521903927484929681108 * q^65 + 19080130794608880088211092 * q^66 + 19927279436319849143450902 * q^67 - 8373829219145321982498160 * q^68 - 11740592568211854067772156 * q^69 - 5132370883366275255574400 * q^70 + 19086224804727807421919172 * q^72 + 42828123668533070044258924 * q^74 - 81164500905568543837973834 * q^75 - 105896749199037309084347596 * q^76 + 43639762623313421635882292 * q^77 - 98604570863977418199548932 * q^78 - 27720061020991987308873792 * q^79 - 62182770892870708184304728 * q^80 - 581497370030400596903901694 * q^81 - 341107120874158685100150464 * q^82 + 26201266111333778096099838 * q^83 + 507935364828252675231522472 * q^84 + 224109171520266208496093748 * q^85 - 704077428371873697577134268 * q^86 - 681166827660725136677389832 * q^88 + 482826168478152776777239896 * q^90 + 67827511015091818004015876 * q^91 - 83646902794933560160672648 * q^92 + 886600140227681407873186288 * q^93 - 168289477479668477956229936 * q^94 + 239338208955746404979764980 * q^95 - 752456785864472227742519632 * q^96 - 4 * q^97 - 1043862744854197068838248646 * q^98 + 1641925710538879681648895966 * q^99

Decomposition of $S_{28}^{\mathrm{new}}(16, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
16.28.e.a	$16$	$28$	16.e	16.e	$4$	$106$	$53$	$73.897$		None		✓	✓	✓	16.28.e.a	$2$	$0$	$-2$	$-2$	$-2$	$0$		$\mathrm{SU}(2)[C_{4}]$