Space of modular forms of level 16 and weight 28

• Label: 16.28
• Level: 16
• Weight: 28
• Dimension: 119
• Nonzero newspaces: 2
• Newform subspaces: 7
• Sturm bound: 448
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 16 = 2^{4} \)
Weight:	\( k \)	=	\( 28 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(448\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_1(16))\).

	Total	New	Old
Modular forms	223	124	99
Cusp forms	209	119	90
Eisenstein series	14	5	9

Trace form

119 * q - 2 * q^2 + 1594322 * q^3 + 125095688 * q^4 - 1363223164 * q^5 - 59499919472 * q^6 - 217857276024 * q^7 - 287180933804 * q^8 + 35727964216657 * q^9 + 8247210235372 * q^10 + 52508403716462 * q^11 + 1748989708884580 * q^12 - 91357388155780 * q^13 - 7155218316814660 * q^14 - 26159712888157092 * q^15 - 11277270898466024 * q^16 + 38529767492884486 * q^17 - 142926567667036386 * q^18 - 204239143909999798 * q^19 + 442470438134323004 * q^20 - 596151142578540908 * q^21 - 1169169681057307068 * q^22 + 290775780668602136 * q^23 + 10984755246449911984 * q^24 + 12538593095177984699 * q^25 + 17037255844415508360 * q^26 + 13732096803459075392 * q^27 - 60190300783057535720 * q^28 + 13641876929502941540 * q^29 - 676957577616991436364 * q^30 + 167537114447485125264 * q^31 - 1166901104384201893432 * q^32 + 384626372206941245932 * q^33 - 290590654320714186380 * q^34 + 333952533144259767884 * q^35 + 2272823118258680645548 * q^36 + 74248218971412618908 * q^37 - 7667804020978176078752 * q^38 - 14020182433714277806664 * q^39 - 13361029860556314821176 * q^40 + 4328237062700559453618 * q^41 - 46808273599641292573640 * q^42 + 42076459836156774818230 * q^43 + 78151525061974584923236 * q^44 - 3293567904709183829184 * q^45 - 30741189488837489213204 * q^46 - 182762104415596157357312 * q^47 - 189351174993879449193752 * q^48 - 804138151222650262931565 * q^49 + 548328807383867462419206 * q^50 - 240486203962843239536884 * q^51 - 870962460180776269413356 * q^52 + 168407761201415131686940 * q^53 + 1136059014139929162305056 * q^54 + 862766662205475383168072 * q^55 + 1200724087407057566405656 * q^56 + 347209001262435906951184 * q^57 - 2828993593282901350448872 * q^58 - 729623503432382371914314 * q^59 + 7255680995179605171006528 * q^60 - 4521437336569426323761956 * q^61 - 3746979776437258967395280 * q^62 + 6939134737403113766417772 * q^63 - 998638142638832585325568 * q^64 + 1077447880791548538582424 * q^65 + 19080130794608880088211092 * q^66 + 26241587393503106031256874 * q^67 - 8373829219145321982498160 * q^68 - 9086820423405249011485596 * q^69 - 5132370883366275255574400 * q^70 - 19706403758963548293385784 * q^71 + 19086224804727807421919172 * q^72 - 9932524710958800418619246 * q^73 + 42828123668533070044258924 * q^74 - 13342508631674452147416318 * q^75 - 105896749199037309084347596 * q^76 + 106652527248041237755694996 * q^77 - 98604570863977418199548932 * q^78 - 38226399093462318840916336 * q^79 - 62182770892870708184304728 * q^80 - 438463939948584580703370249 * q^81 - 341107120874158685100150464 * q^82 - 111100540189692880281345758 * q^83 + 507935364828252675231522472 * q^84 + 212613134774958059843048288 * q^85 - 704077428371873697577134268 * q^86 + 392968440170718813397001592 * q^87 - 681166827660725136677389832 * q^88 + 154781360132432588744505474 * q^89 + 482826168478152776777239896 * q^90 - 104130293217041327294208076 * q^91 - 83646902794933560160672648 * q^92 + 850640003985501774560467568 * q^93 - 168289477479668477956229936 * q^94 + 413944223535146470728320428 * q^95 - 752456785864472227742519632 * q^96 - 149155906667981004872164682 * q^97 - 1043862744854197068838248646 * q^98 + 3358780747001683142160314026 * q^99

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_1(16))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
16.28.a	\(\chi_{16}(1, \cdot)\)	16.28.a.a	1	1
		16.28.a.b	1
		16.28.a.c	2
		16.28.a.d	2
		16.28.a.e	3
		16.28.a.f	4
16.28.b	\(\chi_{16}(9, \cdot)\)	None	0	1
16.28.e	\(\chi_{16}(5, \cdot)\)	16.28.e.a	106	2

Decomposition of \(S_{28}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{28}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{28}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)