Space of modular forms of level 4 and weight 51

• Label: 4.51
• Level: 4
• Weight: 51
• Dimension: 24
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 51
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 4 = 2^{2} \)
Weight:	\( k \)	=	\( 51 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(51\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{51}(\Gamma_1(4))\).

	Total	New	Old
Modular forms	26	26	0
Cusp forms	24	24	0
Eisenstein series	2	2	0

Trace form

24 * q - 17860140 * q^2 - 929666293798128 * q^4 - 138405874550121360 * q^5 - 56152801168471557984 * q^6 + 14626199637492363754560 * q^8 - 4777705768255413501953832 * q^9 + 27499248123076878592047240 * q^10 - 2216937833132038153955529600 * q^12 + 11302926238113456056731311600 * q^13 - 64098077924292339626310394944 * q^14 - 467729592512594226142269325056 * q^16 + 2656265948195011490140059040560 * q^17 + 39434470599039326712183785703540 * q^18 + 339905907831268134363726728180640 * q^20 + 169603538062746157629606324483072 * q^21 + 6347144082078959503784125785295200 * q^22 + 9079405518920841853662995144372736 * q^24 + 475176337905115644064646560538543880 * q^25 - 589115599277237002677037694854124088 * q^26 + 1934997915538177044738411909667203840 * q^28 + 3888403954206498652438025077201941744 * q^29 - 49809563203381609114811567947524634560 * q^30 + 93859567928466936552940433258797286400 * q^32 - 84814353269952137621931006269490347520 * q^33 - 331419812994692320859806572476381143512 * q^34 + 2180883143606453496636073550648131535760 * q^36 - 1915970376671965110829438561948138603920 * q^37 + 6924669358079016649548416227687554270240 * q^38 - 27342889565607897985673462156586098037120 * q^40 - 57490083518603310743169338137325347098192 * q^41 + 82946402854618434295889854857593010593280 * q^42 - 121834225107577054434960720818972723479680 * q^44 + 346877798333463328934090287021830695612400 * q^45 - 218732732005258960716057022723111519268544 * q^46 + 6201056104461075721019556161533742427555840 * q^48 - 8490133470606194677358826333143435688556392 * q^49 + 1009457809161004668964223318660303022156060 * q^50 - 1675616205991024926531430113577608655190880 * q^52 - 15053813315982454995239498703058997883188880 * q^53 + 20083378732208960985886577203449501482210112 * q^54 - 147467808128093589295976776841887661872763904 * q^56 + 265244243468483428781272922064640087736501760 * q^57 + 30488791239882897657654312680940289781810760 * q^58 + 668439066652000767490111200140281264624968960 * q^60 + 289331369660634110907893060991527292225397488 * q^61 - 1673139441143029020972919042211642178581402880 * q^62 + 381582032189653235332737651828165925520412672 * q^64 + 1440559938642695885976666282458411937446383200 * q^65 + 1434668205565146435464893911070441833599527680 * q^66 - 544132285314324163826631362310232172916672480 * q^68 + 19135265064252706425726217403554458930998295552 * q^69 + 38543167027510182371063705764281361497148195200 * q^70 - 27695238672534378322403408359051014487119307200 * q^72 - 51848129887014825814619624537458903588125491280 * q^73 + 14907981579863585669411994256926897823640037768 * q^74 + 337128579555044603708310432913036429444065628800 * q^76 - 219787867313477340634638450885239740387763942400 * q^77 - 81325253079080039183213851445244998600450911680 * q^78 + 117746336855493789034029131383731103265247582720 * q^80 + 2326639692951745802361303835163827802615809410456 * q^81 - 389197716424902775697226339085417039858385661720 * q^82 - 4014187559277166406940825093800428258475993131008 * q^84 - 423737047769126479417398957959176723332088891680 * q^85 + 2341899386954237078162640105778950497458103562336 * q^86 - 3554596769806703352430936265096913958570280440320 * q^88 - 11194716447985328806146021261495165161098509665616 * q^89 - 14759307283758985582055297483426951648728703451960 * q^90 + 57746687695986263756269583165434364832264168986880 * q^92 - 36382571980796542594302791779137194908836657623040 * q^93 + 19224785241848303155448807036447000065534842477696 * q^94 - 80880431007869106858400527918653060183467566096384 * q^96 + 87153057884802800512123005165247218349991573985840 * q^97 - 33621071814412228695327520379309327750605952274540 * q^98

Decomposition of \(S_{51}^{\mathrm{new}}(\Gamma_1(4))\)

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
4.51.b	\(\chi_{4}(3, \cdot)\)	4.51.b.a	24	1