Space of modular forms of level 6 and weight 51

• Label: 6.51
• Level: 6
• Weight: 51
• Dimension: 16
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 102
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	=	\( 51 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(102\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{51}(\Gamma_1(6))\).

	Total	New	Old
Modular forms	52	16	36
Cusp forms	48	16	32
Eisenstein series	4	0	4

Trace form

16 * q + 1253053221840 * q^3 - 9007199254740992 * q^4 - 32932351638918660096 * q^6 + 367414010494781657120 * q^7 + 1218450439681151198460048 * q^9 - 7520718129277809784258560 * q^10 - 705406252869252932519854080 * q^12 + 14473602931619533230795113120 * q^13 + 216833777201469524020577049600 * q^15 + 5070602400912917605986812821504 * q^16 + 16538975536840422718694102138880 * q^18 - 185189327557714417912488806166112 * q^19 - 1351649736247953504366541661187168 * q^21 - 764105650767146579441053020979200 * q^22 + 18539265821183527605562274010365952 * q^24 - 112382335366036304714641238842413680 * q^25 - 712341964321945028181375013490762160 * q^27 - 206835700094374772210543564884541440 * q^28 + 3231744390229988428792807329166786560 * q^30 - 2951364891650852050343473186804986592 * q^31 - 222529127541398780879120602813363952640 * q^33 + 17080177354443878870311402780980412416 * q^34 - 685926618264681193801922867703343742976 * q^36 + 5184997534119803692343688829956183850400 * q^37 - 23282857940363286579753439240648763727840 * q^39 + 4233787920571759738473589087673222430720 * q^40 - 86848333524273331695290857761549456506880 * q^42 + 236522569956631127789954180309184223106720 * q^43 + 155789534172431550876156267807128621598720 * q^45 + 658466148847806302611409196544414810374144 * q^46 + 397108417195848172716014717408663002152960 * q^48 - 1793532810012402091655193423926404641424080 * q^49 + 17951885000044631237190695842465552020860928 * q^51 - 8147914096193781044484535868066434058813440 * q^52 + 9050236522717406679986481041941375462932480 * q^54 - 45102911438036757653944888934246846303139840 * q^55 + 58175617851157007129781194505323601060828960 * q^57 + 150604340811632684029475047745479332562206720 * q^58 - 122066564775734412418621749209356026721075200 * q^60 + 1638492436359088579096062716108443835214014624 * q^61 - 1202917062582127944743445309649927910668996320 * q^63 - 2854495385411919762116571938898990272765493248 * q^64 + 385080915882004288340309040218419133983752192 * q^66 - 6183171734658027442966268618380998317940588640 * q^67 + 26177180576637342118655455741535294046337431552 * q^69 - 32317593281387502991404341604175192477705175040 * q^70 - 9310615508100534599366289196918145032975810560 * q^72 - 73966260215056293459980307381222511735256255200 * q^73 + 26594788370441960173383521992074077411659805520 * q^75 + 104252323322739422323253708383785344496192978944 * q^76 - 258582623887823444169659672664554492600537579520 * q^78 + 1381894725771336189422902060071593401412263376672 * q^79 - 626845441680707512652650921616428490271703700208 * q^81 + 10214987713262111584584507130947552344706908160 * q^82 + 760911156062714075307427709769534550161192124416 * q^84 + 596654665163372492678097043631590631308928409600 * q^85 + 4508750095901352823906182845473477897746751165440 * q^87 + 430153240508326460776459624108217584352388710400 * q^88 + 6763284035678336702485034529903786884567610163200 * q^90 - 23886398871230156665592273667475154962108118809280 * q^91 + 893096335690535702536061397703462361064335559840 * q^93 + 42795430383341022122836255619653281929041627054080 * q^94 - 10436678830500588431579959075263286979055555969024 * q^96 + 143852742929877989785036869333722693336796775876640 * q^97 + 19138128440427533755011482935322788870838529841152 * q^99

Decomposition of \(S_{51}^{\mathrm{new}}(\Gamma_1(6))\)

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
6.51.b	\(\chi_{6}(5, \cdot)\)	6.51.b.a	16	1

Decomposition of \(S_{51}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{51}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{51}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{51}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{51}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)