Space of modular forms of level 12 and weight 27

• Label: 12.27
• Level: 12
• Weight: 27
• Dimension: 35
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 216
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	=	\( 27 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{27}(\Gamma_1(12))\).

	Total	New	Old
Modular forms	109	35	74
Cusp forms	99	35	64
Eisenstein series	10	0	10

Trace form

35 * q - 362 * q^2 - 606603 * q^3 + 25515260 * q^4 + 597551756 * q^5 - 13350860802 * q^6 - 147536142318 * q^7 - 1107070096304 * q^8 - 19931792947677 * q^9 + 26931976009684 * q^10 + 109272086034228 * q^12 - 603701373423218 * q^13 + 313063132413000 * q^14 + 776795835576960 * q^15 - 3100079273957392 * q^16 + 2133272788873220 * q^17 + 306718476618366 * q^18 - 52597695713067126 * q^19 + 264764444929804808 * q^20 - 104445790013928030 * q^21 - 92218429234595976 * q^22 - 1919082130689489984 * q^24 + 7343724333948495903 * q^25 - 2629533823962194452 * q^26 + 7289336541510051453 * q^27 + 9919587622044293808 * q^28 + 35336802183890204828 * q^29 + 20705214404728454148 * q^30 + 12878568721772821026 * q^31 + 94898944398551558368 * q^32 - 52731224865128053944 * q^33 + 250889584329058982236 * q^34 - 21618789164976600180 * q^36 + 632617208647512981358 * q^37 - 339324321912166786968 * q^38 - 418990993009914444846 * q^39 + 1204895166274342327648 * q^40 - 3174272308641920782492 * q^41 - 1874581468922169789624 * q^42 + 1059517791744831344538 * q^43 - 6919453982552367149616 * q^44 + 344100851346139642332 * q^45 - 9972929435324351907936 * q^46 - 68138765476578082512 * q^48 - 24969954241376837020987 * q^49 - 11047982507126957077518 * q^50 + 21604271277632412188160 * q^51 - 16568950607247541776008 * q^52 - 24786573079700991801028 * q^53 + 11312032283793635753286 * q^54 - 17061665554147935663360 * q^55 + 200089699190068058042112 * q^56 + 45767126537363169995610 * q^57 - 220598175449855405163068 * q^58 + 72866395018508472946584 * q^60 + 206146795968470773580254 * q^61 - 623372947172755981947336 * q^62 + 64768665360724216249698 * q^63 + 1080818356201959029978240 * q^64 - 1316295254014450273680488 * q^65 - 1329614006131795155458184 * q^66 + 29668351083150543562602 * q^67 + 2415795996476641019961560 * q^68 + 597563260288658863577568 * q^69 - 8425804120532243848777872 * q^70 + 938007882453344253798672 * q^72 - 2358740973535144020767498 * q^73 - 11763874228804735141834756 * q^74 - 1591486849862375849623155 * q^75 + 15310911277987916603567472 * q^76 - 10483653949388872706482464 * q^77 - 5626948710786262226037828 * q^78 - 664568686502876098112958 * q^79 + 68210093156625054246712352 * q^80 + 21738559160520285120049923 * q^81 - 56773791814157835896376836 * q^82 + 26707568516986008270896208 * q^84 + 17645951989243029952874360 * q^85 - 81429891139181858956862280 * q^86 - 23844871160850093632530560 * q^87 + 141540167560176007465501440 * q^88 + 66149620842144824031833300 * q^89 - 22819156502797392261846012 * q^90 - 11631425068119275566874316 * q^91 + 185442549903771884596696512 * q^92 + 59371564273125985760476674 * q^93 - 289082417212177377756906192 * q^94 + 102525474487988946129301152 * q^96 - 387099067906720228231002554 * q^97 - 146287003251689608976577002 * q^98 - 36097304313493837879407360 * q^99

Decomposition of \(S_{27}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.27.c	\(\chi_{12}(5, \cdot)\)	12.27.c.a	1	1
		12.27.c.b	8
12.27.d	\(\chi_{12}(7, \cdot)\)	12.27.d.a	26	1

Decomposition of \(S_{27}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{27}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{27}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)