Space of modular forms of level 12 and weight 22

• Label: 12.22
• Level: 12
• Weight: 22
• Dimension: 43
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 176
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	=	\( 22 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(176\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(12))\).

	Total	New	Old
Modular forms	89	47	42
Cusp forms	79	43	36
Eisenstein series	10	4	6

Trace form

43 * q - 59049 * q^3 + 1212040 * q^4 + 17559810 * q^5 - 73477608 * q^6 + 791583864 * q^7 + 15323110971 * q^9 + 70993722608 * q^10 - 112222937772 * q^11 + 230311800264 * q^12 - 725726689846 * q^13 - 2367628113510 * q^15 - 3296861950688 * q^16 + 2953244684214 * q^17 - 38138435545488 * q^18 + 25208162419020 * q^19 - 7103241137688 * q^21 + 345245332418448 * q^22 + 157775918327784 * q^23 + 162733136355360 * q^24 - 2435622081669483 * q^25 - 205891132094649 * q^27 + 3010485857135664 * q^28 - 4359534278069718 * q^29 + 5225832293639088 * q^30 + 3420045112432992 * q^31 - 4927403988048540 * q^33 - 11653770049992256 * q^34 + 58943170624401360 * q^35 - 18580578856893912 * q^36 - 25597840292902990 * q^37 + 21271071576651570 * q^39 - 89660451263290816 * q^40 - 58021202638110690 * q^41 - 196777060056297264 * q^42 + 91890557649844404 * q^43 + 551884209200145186 * q^45 - 24590270471085024 * q^46 + 639021428445851856 * q^47 - 1070121602451491040 * q^48 - 720260396448882941 * q^49 + 76201133615357022 * q^51 + 1474695233111072240 * q^52 - 605389055944970862 * q^53 - 107978656785090264 * q^54 + 223229472927915960 * q^55 - 2442884146037356212 * q^57 + 9260173307858336144 * q^58 + 111533213628510372 * q^59 + 6491621502020133696 * q^60 - 19491067201098601510 * q^61 + 2760082269078505464 * q^63 - 2949437838551773568 * q^64 - 15411720181369637700 * q^65 + 1836224451373338192 * q^66 + 5308269714319267356 * q^67 + 27358457849854520520 * q^69 - 24886444039106795232 * q^70 + 31114565784489756600 * q^71 - 27969226308253542336 * q^72 + 99199950295188522446 * q^73 - 67005681755538219975 * q^75 + 22386121373924673552 * q^76 + 8172031342996112544 * q^77 + 76385487692811283152 * q^78 - 115367151634837499856 * q^79 - 439745179763386019637 * q^81 + 1864686882869863520 * q^82 + 224057353676040396684 * q^83 + 311685180307346738352 * q^84 - 106440038069048215004 * q^85 - 7791544403279033886 * q^87 + 15063645347500158144 * q^88 + 751807239847095025710 * q^89 - 159737520743388593232 * q^90 - 697445725818940231920 * q^91 + 107616993980455324464 * q^93 + 242051617770611035200 * q^94 + 519788551712918229000 * q^95 - 1187951481218430818688 * q^96 - 1385685814566059051914 * q^97 - 391297188857803294572 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(12))\)

We only show spaces with even 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
12.22.a	\(\chi_{12}(1, \cdot)\)	12.22.a.a	1	1
		12.22.a.b	2
12.22.b	\(\chi_{12}(11, \cdot)\)	12.22.b.a	40	1

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 1}\)