Space of modular forms of level 11 and weight 37

• Label: 11.37
• Level: 11
• Weight: 37
• Dimension: 175
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 370
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 11 \)
Weight:	\( k \)	=	\( 37 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(370\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{37}(\Gamma_1(11))\).

	Total	New	Old
Modular forms	185	185	0
Cusp forms	175	175	0
Eisenstein series	10	10	0

Trace form

175 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 - 5 * q^5 - 59374855782405 * q^6 - 1070220600658805 * q^7 - 29176571835187205 * q^8 + 128019205583139515 * q^9 - 6286497787237449605 * q^11 - 144335420254899404810 * q^12 + 44327529861949875595 * q^13 + 2031839586177124543690 * q^14 - 2165946298191110606845 * q^15 + 8458401943369901708095 * q^16 - 7490327325813480430805 * q^17 - 60837982078161281704830 * q^18 - 326678743806816002363105 * q^19 + 1147562561947819990646700 * q^20 - 6063754499010023831256155 * q^22 + 8029676088646924887970190 * q^23 - 50055945555290769165286735 * q^24 + 35128221580843457970463195 * q^25 + 21988865804670072662802970 * q^26 + 100642038855502159492943695 * q^27 - 127876974742545752186587580 * q^28 - 148260196183604243748987605 * q^29 - 1070759340366247069104541940 * q^30 + 1939732807800079453128035395 * q^31 - 3516154521178412288028738105 * q^33 - 7279046812459318321831478950 * q^34 - 23197744423447187485441354565 * q^35 + 14523856704867737635739095230 * q^36 + 31303140288083270798436910795 * q^37 - 155405901143330313812233615580 * q^38 + 286031400792060638653556313515 * q^39 - 477426765741289836914144479140 * q^40 + 379575514551175813164655289875 * q^41 + 409334530698727144748760766550 * q^42 + 2239487064072846524564751906400 * q^44 - 5774438021199947870000052445810 * q^45 + 6471635931859176991281379026230 * q^46 - 4958486225784959003034352412405 * q^47 + 15027693122549835924618690632640 * q^48 - 8516924327929909314437275975565 * q^49 + 4301789368025358745934822554095 * q^50 + 20279393467491519090651771230415 * q^51 - 4768877018299335276912900819530 * q^52 + 37580979009579979674884139475195 * q^53 + 17305200065426315660479401106315 * q^55 + 103684849287591640563520203120020 * q^56 - 356294378665060763444626736899305 * q^57 + 282239352726836493871144276414420 * q^58 - 445576590624464703606561144339785 * q^59 + 1210411453027989893100395256207460 * q^60 - 586089435783888962935931167143125 * q^61 - 1353966157408751988132132606766280 * q^62 + 1480985498760577661292719775942000 * q^63 - 2476460469535824956376064413007305 * q^64 + 4921342949570636107387541010624750 * q^66 - 2180127199313399692340049874653610 * q^67 + 498222323619934659338609978515640 * q^68 + 4668126968584011175156470472753270 * q^69 - 9555268720385952298883618757815580 * q^70 + 3678124853450588744508267914287195 * q^71 - 21173003953155614160217885635057035 * q^72 - 9121494655353489880552044964558205 * q^73 + 54587485956456511316304351104621110 * q^74 - 51208879822735560834664969205012745 * q^75 + 59599538614824041496327724954088995 * q^77 - 172308108699245094217407412105350560 * q^78 + 125594453280400514161996671785442235 * q^79 - 152435440532095376024678996311453260 * q^80 + 42060657242167294766526593380235255 * q^81 - 44083766737736328322989271946772455 * q^82 - 30360136010152883736107815952967905 * q^83 - 25232000762471146121079708018896310 * q^84 + 159912389420064694480973325765328795 * q^85 - 77573094715582774137380621232418365 * q^86 + 121404259418248345938770091800487595 * q^88 + 195311242781591954446623058532893790 * q^89 - 1547101391675638388793205349681920400 * q^90 + 833886854520510059588912218877270515 * q^91 - 686203170379872859044237093266833660 * q^92 + 110638431939788867034223004066461995 * q^93 - 1759596618568751910060951203115934280 * q^94 + 1879971118719345940339121985440360635 * q^95 - 4525788807697749593655423159638140820 * q^96 + 1762591133028968561539464972472874695 * q^97 - 2324458940196645883893757396468221085 * q^99

Decomposition of \(S_{37}^{\mathrm{new}}(\Gamma_1(11))\)

We only show spaces with odd 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
11.37.b	\(\chi_{11}(10, \cdot)\)	11.37.b.a	1	1
		11.37.b.b	34
11.37.d	\(\chi_{11}(2, \cdot)\)	11.37.d.a	140	4