Space of modular forms of level 12 and weight 51

• Label: 12.51
• Level: 12
• Weight: 51
• Dimension: 67
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 408
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	=	\( 51 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(408\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{51}(\Gamma_1(12))\).

	Total	New	Old
Modular forms	205	67	138
Cusp forms	195	67	128
Eisenstein series	10	0	10

Trace form

67 * q + 35720278 * q^2 - 88437661203 * q^3 + 1780736619398204 * q^4 + 276811749100242716 * q^5 + 29345883352488777150 * q^6 + 1346835075664713827362 * q^7 + 917394449569278456976 * q^8 - 13111105679315333077586877 * q^9 - 31912475515972849473437996 * q^10 + 476418932797763703125340468 * q^12 - 6956358736007382994348638418 * q^13 - 352576455536977914693058296 * q^14 - 91755057863258810998685925120 * q^15 - 11026342603351015801016881168 * q^16 - 4503009195039304872787896813580 * q^17 - 8547838565331184268630990803074 * q^18 - 19010962381103270316700559904518 * q^19 - 1779989763579433400445833705823352 * q^20 - 1197335704527060274333626347479758 * q^21 - 10804067204886818345289015433946376 * q^22 + 26786176587058804308795199636121472 * q^24 + 278720723511309350912795706380990543 * q^25 + 272506049893317769487858989223460140 * q^26 + 1265903921694044758964309067883149333 * q^27 - 3640628018429803526673827059994196432 * q^28 - 1575543655613720021096885659281260692 * q^29 + 22011520714135758531229467554361941508 * q^30 + 38180226204043801819855852602294805618 * q^31 - 182666520246944104743892028660189683232 * q^32 - 161584429484547341609566331329665695064 * q^33 + 202180387307760107108445429119250441052 * q^34 - 426129078558387681021325680102266410932 * q^36 + 2841362835431455699592942855405387485838 * q^37 - 11777624579575660743222375955764120086808 * q^38 + 5898863342088107216420848512205815756642 * q^39 + 35004713977169840263384830352189914673888 * q^40 + 64571724898167265760648077893181647458900 * q^41 - 77662538183224779883743525531770796549624 * q^42 + 120137748253649168343710363733229971463498 * q^43 + 25992076779039939351884496058595364474576 * q^44 - 332021854667483812511857359178519532711508 * q^45 - 113341294871845837916247795178773497527776 * q^46 + 107134777580343728152807268811544385057328 * q^48 - 8363032936979658880819862417839256913281611 * q^49 + 9395543008935723858784277600535470196818802 * q^50 + 1336516162088228868225552286664441856199680 * q^51 + 19038038585126185444573656316525484943023992 * q^52 - 1582053423736783089249579847210497429809908 * q^53 - 7022450201930509974415237022851297437003450 * q^54 + 28387755703369359493425866079582924077637120 * q^55 + 52491386471536471905134994171245224067034624 * q^56 - 202007702639077751295553011740710378356379830 * q^57 - 110739383398291844393628304337013750293500988 * q^58 - 63362030988453307633552068692402175240120936 * q^60 + 14699686350888813479969159270297728249009982 * q^61 + 1517632705352410183206245757251866044333984504 * q^62 + 2254374423668477357845299946802950394017548978 * q^63 - 1312672913647177728666649820434276841831970688 * q^64 - 1925378909911127601512341756911296469648550088 * q^65 + 6885617510983300375038119922547519795087294968 * q^66 + 9979926734994804086559155103836890882269755482 * q^67 + 30374098148288257057881083886026360010643382360 * q^68 - 8695392760640703916242092508512421616622105760 * q^69 - 39043762692778863976832950261802834420484386832 * q^70 - 219531876421819915387833150149926472031769008 * q^72 + 192326821865923113023144836238373686954951309942 * q^73 - 78147025556339027183337058332111213748655580100 * q^74 + 102646864702937555917930587235239375744832950885 * q^75 - 435347149306450562739983351781016071067209800592 * q^76 + 717577906507728414961291823732966342731066625376 * q^77 - 23077825312869207102347273403685521544239256068 * q^78 + 489013646077082116660296803613530143610869312786 * q^79 - 880705790875631565657940699115986387652678522848 * q^80 + 2075195963813540486116146573845246259435131942307 * q^81 - 1461384140929292962021353193970931478689120929156 * q^82 + 777923219358777815900556747508942575279580157904 * q^84 - 549589615695230009951540218465658916362345622760 * q^85 - 12150765127134113445548175135761380151030145851592 * q^86 + 3122454747889097662093742105899335631840614900480 * q^87 - 6034370271504475065238653901164285084567658437120 * q^88 + 7761691515041615074956092853070745893883587839236 * q^89 + 7636633985060807927809383632449712708066596993668 * q^90 - 11443180700839904656096679985629048991502439031148 * q^91 - 5903057871198418318609352424600805670827747330368 * q^92 - 50636731088635332323585766160122033936441771859566 * q^93 + 13778902920839052389770899039198699507500315081136 * q^94 - 61673786094735707806646415370238969615944525976160 * q^96 - 57197861315791966882848851736719075782617392513914 * q^97 - 223055330894159830613661151869033416713064656914602 * q^98 + 63435410054018146732994264871790240111196315742720 * q^99

Decomposition of \(S_{51}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.51.c	\(\chi_{12}(5, \cdot)\)	12.51.c.a	1	1
		12.51.c.b	16
12.51.d	\(\chi_{12}(7, \cdot)\)	12.51.d.a	50	1

Decomposition of \(S_{51}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{51}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{51}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{51}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{51}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{51}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{51}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)