Space of modular forms of level 3 and weight 51

• Label: 3.51
• Level: 3
• Weight: 51
• Dimension: 16
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 34
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 3 \)
Weight:	\( k \)	=	\( 51 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(34\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{51}(\Gamma_1(3))\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	16	16	0
Eisenstein series	2	2	0

Trace form

16 * q - 805889594160 * q^3 - 8928603286542944 * q^4 + 59741521254715126176 * q^6 - 1160438219362916915680 * q^7 - 917133362010787415307120 * q^9 + 9962640343683386458223040 * q^10 + 1075085183344463908563371040 * q^12 - 17571676806780080768406095200 * q^13 - 252478853571109732601797232640 * q^15 + 3949802123446922490774106198528 * q^16 + 30986337565141206025856558391360 * q^18 + 1379828669138141746892931439520 * q^19 - 111396505340010481102602793602144 * q^21 - 8697014882967219827745097642155840 * q^22 - 24856068729411443245590195724389888 * q^24 - 247177690635772886940456671461616240 * q^25 - 566225857063459393265304567639077040 * q^27 - 2842471859105181849209658608149278400 * q^28 - 95083663021298497062849488385718080 * q^30 - 32456713273539003343133275994985596128 * q^31 + 208164420072841391596617211869430763520 * q^33 - 33249966810885190980547256098343086848 * q^34 + 4952549477583140623264007678836430884512 * q^36 - 6104886101483403140491466019701008628320 * q^37 + 14319878911854660536221977416655968952864 * q^39 - 79378427377259757231754149421152231674880 * q^40 + 220193985372945422075170374409554434345280 * q^42 - 239912780755161074874070897685354604093280 * q^43 + 404294473867486571097383172202940594626560 * q^45 + 400127974367978302927117199310824860747392 * q^46 - 195852205157194888733291535633940078487040 * q^48 + 7756742979719884587662335732343624450217264 * q^49 - 22816787357045532507604701216001119049826304 * q^51 + 34540208412794675711241918534166219141682240 * q^52 - 37078899550062822143707097150604573228332064 * q^54 + 45216264103214796600551728427982096094187520 * q^55 + 115271948993831969696350738311555975411528480 * q^57 + 43522489698793274707107654613719524104330560 * q^58 + 1354484536535639998326967964597877017810365440 * q^60 - 1032839001229161735403869047098441027705745248 * q^61 + 1265275338837677100087764662397490903677394720 * q^63 - 4542515152397444245352575462117208315566579712 * q^64 - 4657485477249020490936694996132059449650482240 * q^66 - 3817434864999169276654492542337801503847243360 * q^67 - 29108900678903921076875303210771614631779590144 * q^69 + 66687139423174962971147483898200364211819071360 * q^70 - 50951496893426096064329891422987565275697679360 * q^72 + 62840636707457285193832380671992749644492936480 * q^73 - 38584347439641248810951754279507290957506841520 * q^75 - 379952487102413183635490377164888694697164159936 * q^76 + 833109584730538251138946660120225510614282177600 * q^78 - 830747904876447921018614330884133699799138761440 * q^79 + 1032228380797488490329349278568250608960792935696 * q^81 + 1231548950774518973407703338755523137299731098240 * q^82 - 339734219896283183630107828604099861173792790976 * q^84 + 2049530912316692604343314288618091154545891000320 * q^85 - 6598252053059881258332508150603860072574023014400 * q^87 + 13874433256726455880774207842929237210014877506560 * q^88 - 22445385894887515269963508686712895401166011160640 * q^90 + 2635882670657373152254751588180146395473977659712 * q^91 - 8484744406469934701926687045714291237966868515680 * q^93 - 93345961851335615506160035483618441199551556460288 * q^94 + 132276510146286261086666434305825056842259686268928 * q^96 - 25584956942431598928687153545624051154443053105120 * q^97 + 76236825461197768189828239409441204642028540743680 * q^99

Decomposition of \(S_{51}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.51.b	\(\chi_{3}(2, \cdot)\)	3.51.b.a	16	1