Space of modular forms of level 12 and weight 57

• Label: 12.57
• Level: 12
• Weight: 57
• Dimension: 75
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 456
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	=	\( 57 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(456\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{57}(\Gamma_1(12))\).

	Total	New	Old
Modular forms	229	75	154
Cusp forms	219	75	144
Eisenstein series	10	0	10

Trace form

75 * q + 399000966 * q^2 - 7329808306821 * q^3 - 113563996432917940 * q^4 + 27528390816262670544 * q^5 + 4513603916613995168238 * q^6 + 177681777818173258912886 * q^7 + 45877428410728137175910880 * q^8 - 9397659986386441745884812693 * q^9 + 1721979730348558838032279828 * q^10 - 114244276986970331919069231180 * q^12 + 19812704047083256542162727300662 * q^13 + 397905751088196754357968060414840 * q^14 + 1395067724970473591422723870224480 * q^15 + 2687501047969341810015021463776368 * q^16 - 64764931269895074322839838834760400 * q^17 - 69605403710576786259490015043709762 * q^18 - 1004501306938610564589075299496005194 * q^19 - 5169033452569342894200200728344497688 * q^20 - 24201170870262869228035390482753306330 * q^21 + 56895690120551096449451986476501043032 * q^22 - 879937930535365577736919604589664445136 * q^24 + 6454752051421817453954249165470635584347 * q^25 - 646459020218225590272610770833309887812 * q^26 - 29511946094553159036805339561224201354021 * q^27 - 32049869534361719302696010816976733170672 * q^28 - 286052870649752520294761114033844752644848 * q^29 - 222257623171953605396585648774722774962300 * q^30 + 1107881329510860402824021545446975057432566 * q^31 - 1248076529946248681360107886995765482655584 * q^32 - 14170975930604444740719623897714862769903680 * q^33 - 20711722411635332686336655892306966889468196 * q^34 + 19811149576765073044251320308188221279195580 * q^36 + 33319922858002974352380290390057537360050230 * q^37 - 583128370931071195882757371925790940999971960 * q^38 + 287964321657765322657280396929000405207440726 * q^39 + 3574974410569425207807617916244746585535935424 * q^40 - 780967505366685843918304593773376708871391952 * q^41 - 5260177359002168070138255134893896868555141128 * q^42 - 513925938590879562291699517557997741144331914 * q^43 - 31014584429140565588044052656971485142913150704 * q^44 - 32976713350763235485195345053531817594787121968 * q^45 + 49425044353811597430908814150924739307596678464 * q^46 - 218812600904558892905382039983081155881694583952 * q^48 - 1318019057122112712524863989464732974957559001103 * q^49 + 1433465844523634304619297452250453300940297150802 * q^50 + 1819115237742486563793183486533541599929403702400 * q^51 - 4971329022744948218382361214019915775738004375432 * q^52 - 3430624886841175492242483826309294785691177755888 * q^53 - 787394642060986124632787549200069434021048756666 * q^54 - 9780647440218234016300876478840193091368641730240 * q^55 + 20848616759460559282629283904345953394929356693312 * q^56 - 18275883740721312517928624138371850797308244245018 * q^57 - 81661495721142318775077024760058202280803462143804 * q^58 - 144884345026075616914549301445649737235673650412904 * q^60 + 566282046295699800346698042390438368500966337586294 * q^61 - 649351254627803738152224490422265647279661147484184 * q^62 - 58834910560508848666374607858714159872742012415754 * q^63 - 1483798832619097806856413431167683434213560707468160 * q^64 + 23935414283497579725645177339392354153986987115808 * q^65 + 2027590021542423232034469297725749421689707214409496 * q^66 - 5071990146344428693216954952741541310639615987812874 * q^67 - 39848616773915163234856402598887897357836598912584 * q^68 - 5861940296927842451381504197608360648733575076561728 * q^69 + 8631083563051822838039808400656400583665830751383696 * q^70 - 8003281189378917828268067193544267475622645516416160 * q^72 + 75178013023852379182872548887310568944339708409707478 * q^73 - 107670079862146323894678533297869808317262188252235124 * q^74 - 12688669132601316922399956992144137433871120481600485 * q^75 + 140881680631581015838737961758175629466465333600836912 * q^76 - 136687335601170613815148327060862060688582880416465792 * q^77 - 166965440932564989227226677221068265521624153264395700 * q^78 + 218422043205801415668769077090026105030579951755609718 * q^79 - 1307083589963006343003478238889043235884283174412930528 * q^80 + 2195944331471935944281052605445782047526587425080686923 * q^81 + 380325520390871021428960198556385158856662280741737500 * q^82 + 425723379961415896586484823177762358696950202859957552 * q^84 + 3660510289425368570838756940314385813500097212819578144 * q^85 + 4378639852252254220807133199051754173078139544176875480 * q^86 - 2497104188647261429795020226479797205678943256710810080 * q^87 + 4421796391748181727471191564877402810679327940985402560 * q^88 + 4197897116024898144535731178195291665783268518395779440 * q^89 - 300398005333003607779512767973332327031537449724632796 * q^90 - 10608806552130509393178878215362900035628529774025549396 * q^91 + 31846247555339051094596089978682453203770613980997775616 * q^92 + 19690529691630194811968598806451301996964289380165096550 * q^93 - 14421590428333061780365248465352892547219706040579921328 * q^94 - 57982428924402904531852855494855812088509942962853779488 * q^96 + 26812611067359080629072760559065988163096574640802271574 * q^97 + 53490267464390364314429847632793925961866818005238331110 * q^98 - 62928614165687861198860145697172941089051505953409384000 * q^99

Decomposition of \(S_{57}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.57.c	\(\chi_{12}(5, \cdot)\)	12.57.c.a	1	1
		12.57.c.b	18
12.57.d	\(\chi_{12}(7, \cdot)\)	12.57.d.a	56	1

Decomposition of \(S_{57}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{57}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{57}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{57}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{57}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{57}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{57}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)