Space of modular forms of level 21 and weight 12

• Label: 21.12
• Level: 21
• Weight: 12
• Dimension: 124
• Nonzero newspaces: 4
• Newform subspaces: 10
• Sturm bound: 384
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(21))\).

	Total	New	Old
Modular forms	188	136	52
Cusp forms	164	124	40
Eisenstein series	24	12	12

Trace form

124 * q - 156 * q^2 + 240 * q^3 - 16270 * q^4 + 25926 * q^5 - 8748 * q^6 + 95858 * q^7 - 364362 * q^8 - 95316 * q^9 - 1006992 * q^10 + 2168754 * q^11 + 1044816 * q^12 - 4578450 * q^13 + 911016 * q^14 + 7289892 * q^15 + 4986418 * q^16 - 20915472 * q^17 - 57373326 * q^18 + 9829158 * q^19 + 208941924 * q^20 - 25021878 * q^21 - 281709120 * q^22 - 33942648 * q^23 + 219544560 * q^24 + 125172514 * q^25 - 85963782 * q^26 - 28697814 * q^27 - 778785110 * q^28 + 55035312 * q^29 + 875231910 * q^30 + 1065240054 * q^31 + 141397422 * q^32 - 1210649112 * q^33 - 2998330044 * q^34 - 188269086 * q^35 + 3154221258 * q^36 - 522351176 * q^37 + 2863053174 * q^38 + 1146290466 * q^39 - 2321750904 * q^40 - 5108017836 * q^41 + 917605998 * q^42 + 451400800 * q^43 + 8634464472 * q^44 + 3069855756 * q^45 - 5226631068 * q^46 - 9119839962 * q^47 - 3744664992 * q^48 + 534491554 * q^49 + 12401784402 * q^50 + 5012082180 * q^51 + 18419178168 * q^52 - 4383832044 * q^53 + 9890068410 * q^54 - 31418985240 * q^55 - 50897831022 * q^56 - 16794190368 * q^57 + 29905504488 * q^58 + 41910542316 * q^59 + 21727277460 * q^60 - 10966065750 * q^61 - 72062486652 * q^62 - 5074714218 * q^63 + 93180789446 * q^64 + 34131921774 * q^65 + 11522305242 * q^66 - 10589572102 * q^67 - 85753019328 * q^68 - 30094945416 * q^69 - 128723772144 * q^70 + 37983065484 * q^71 + 148141686510 * q^72 + 118013887524 * q^73 - 27646219962 * q^74 - 29432293854 * q^75 + 61658709192 * q^76 - 3437989608 * q^77 - 130373153568 * q^78 - 200997166690 * q^79 - 167865734184 * q^80 + 47387357496 * q^81 + 188065740024 * q^82 + 327381542364 * q^83 + 442338340908 * q^84 - 28003464792 * q^85 - 432070908090 * q^86 - 190169349156 * q^87 - 629948449812 * q^88 - 31530231600 * q^89 - 21392271720 * q^90 + 200773225944 * q^91 + 670589880576 * q^92 + 350879210094 * q^93 + 7746670920 * q^94 + 135130970034 * q^95 + 247006314036 * q^96 + 489883921188 * q^97 - 352347190938 * q^98 - 885463275060 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.12.a	\(\chi_{21}(1, \cdot)\)	21.12.a.a	1	1
		21.12.a.b	1
		21.12.a.c	3
		21.12.a.d	3
		21.12.a.e	4
21.12.c	\(\chi_{21}(20, \cdot)\)	21.12.c.a	28	1
21.12.e	\(\chi_{21}(4, \cdot)\)	21.12.e.a	14	2
		21.12.e.b	16
21.12.g	\(\chi_{21}(5, \cdot)\)	21.12.g.a	2	2
		21.12.g.b	52

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)