Space of modular forms of level 1224 and weight 2

• Label: 1224.2
• Level: 1224
• Weight: 2
• Dimension: 18070
• Nonzero newspaces: 30
• Sturm bound: 165888
• Trace bound: 10

Defining parameters

Level:	$N$	=	$1224 = 2^{3} \cdot 3^{2} \cdot 17$
Weight:	$k$	=	$2$
Nonzero newspaces:			$30$
Sturm bound:			$165888$
Trace bound:			$10$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(1224))$.

	Total	New	Old
Modular forms	43008	18610	24398
Cusp forms	39937	18070	21867
Eisenstein series	3071	540	2531

Trace form

18070 * q - 44 * q^2 - 58 * q^3 - 44 * q^4 - 8 * q^5 - 48 * q^6 - 44 * q^7 - 20 * q^8 - 110 * q^9 - 96 * q^10 - 14 * q^11 - 36 * q^12 + 4 * q^13 - 20 * q^14 - 16 * q^15 - 28 * q^16 - 76 * q^17 - 128 * q^18 - 100 * q^19 - 68 * q^20 + 24 * q^21 - 76 * q^22 - 12 * q^23 - 112 * q^24 - 100 * q^25 - 104 * q^26 - 64 * q^27 - 160 * q^28 - 32 * q^29 - 156 * q^30 - 48 * q^31 - 124 * q^32 - 114 * q^33 - 34 * q^34 - 200 * q^35 - 164 * q^36 - 44 * q^37 - 124 * q^38 - 136 * q^39 - 68 * q^40 - 106 * q^41 - 164 * q^42 - 122 * q^43 - 132 * q^44 - 4 * q^45 - 176 * q^46 - 132 * q^47 - 104 * q^48 + 8 * q^49 - 104 * q^50 - 73 * q^51 - 44 * q^52 + 40 * q^53 - 40 * q^54 - 64 * q^55 + 96 * q^56 - 70 * q^57 + 84 * q^58 - 2 * q^59 + 68 * q^60 + 64 * q^61 + 192 * q^62 - 128 * q^63 - 8 * q^64 - 16 * q^65 + 144 * q^66 + 66 * q^67 + 212 * q^68 - 44 * q^69 + 220 * q^70 - 16 * q^71 + 140 * q^72 - 228 * q^73 + 268 * q^74 - 162 * q^75 + 132 * q^76 + 24 * q^77 + 84 * q^78 + 8 * q^79 + 256 * q^80 - 150 * q^81 - 104 * q^82 - 40 * q^83 + 64 * q^84 + 100 * q^85 + 4 * q^86 - 4 * q^87 - 76 * q^88 + 4 * q^89 - 36 * q^90 - 156 * q^92 + 148 * q^93 - 96 * q^94 + 64 * q^95 - 160 * q^96 - 102 * q^97 - 240 * q^98 + 20 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(1224))$

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
1224.2.a	$\chi_{1224}(1, \cdot)$	1224.2.a.a	1	1
		1224.2.a.b	1
		1224.2.a.c	1
		1224.2.a.d	1
		1224.2.a.e	1
		1224.2.a.f	1
		1224.2.a.g	1
		1224.2.a.h	1
		1224.2.a.i	2
		1224.2.a.j	2
		1224.2.a.k	2
		1224.2.a.l	3
		1224.2.a.m	3
1224.2.c	$\chi_{1224}(577, \cdot)$	1224.2.c.a	2	1
		1224.2.c.b	2
		1224.2.c.c	2
		1224.2.c.d	2
		1224.2.c.e	2
		1224.2.c.f	2
		1224.2.c.g	4
		1224.2.c.h	6
1224.2.e	$\chi_{1224}(647, \cdot)$	None	0	1
1224.2.f	$\chi_{1224}(613, \cdot)$	1224.2.f.a	2	1
		1224.2.f.b	4
		1224.2.f.c	8
		1224.2.f.d	8
		1224.2.f.e	12
		1224.2.f.f	14
		1224.2.f.g	16
		1224.2.f.h	16
1224.2.h	$\chi_{1224}(611, \cdot)$	1224.2.h.a	8	1
		1224.2.h.b	8
		1224.2.h.c	56
1224.2.j	$\chi_{1224}(35, \cdot)$	1224.2.j.a	64	1
1224.2.l	$\chi_{1224}(1189, \cdot)$	1224.2.l.a	4	1
		1224.2.l.b	16
		1224.2.l.c	18
		1224.2.l.d	18
		1224.2.l.e	32
1224.2.o	$\chi_{1224}(1223, \cdot)$	None	0	1
1224.2.q	$\chi_{1224}(409, \cdot)$	1224.2.q.a	2	2
		1224.2.q.b	2
		1224.2.q.c	2
		1224.2.q.d	2
		1224.2.q.e	2
		1224.2.q.f	8
		1224.2.q.g	16
		1224.2.q.h	18
		1224.2.q.i	20
		1224.2.q.j	24
1224.2.r	$\chi_{1224}(251, \cdot)$	n/a	144	2
1224.2.t	$\chi_{1224}(829, \cdot)$	n/a	176	2
1224.2.w	$\chi_{1224}(217, \cdot)$	1224.2.w.a	2	2
		1224.2.w.b	2
		1224.2.w.c	2
		1224.2.w.d	2
		1224.2.w.e	2
		1224.2.w.f	2
		1224.2.w.g	4
		1224.2.w.h	4
		1224.2.w.i	6
		1224.2.w.j	6
		1224.2.w.k	12
1224.2.y	$\chi_{1224}(863, \cdot)$	None	0	2
1224.2.ba	$\chi_{1224}(407, \cdot)$	None	0	2
1224.2.bd	$\chi_{1224}(373, \cdot)$	n/a	424	2
1224.2.bf	$\chi_{1224}(443, \cdot)$	n/a	384	2
1224.2.bh	$\chi_{1224}(203, \cdot)$	n/a	424	2
1224.2.bj	$\chi_{1224}(205, \cdot)$	n/a	384	2
1224.2.bk	$\chi_{1224}(239, \cdot)$	None	0	2
1224.2.bm	$\chi_{1224}(169, \cdot)$	n/a	108	2
1224.2.bq	$\chi_{1224}(145, \cdot)$	1224.2.bq.a	4	4
		1224.2.bq.b	4
		1224.2.bq.c	12
		1224.2.bq.d	16
		1224.2.bq.e	16
		1224.2.bq.f	20
		1224.2.bq.g	20
1224.2.br	$\chi_{1224}(287, \cdot)$	None	0	4
1224.2.bs	$\chi_{1224}(253, \cdot)$	n/a	352	4
1224.2.bt	$\chi_{1224}(179, \cdot)$	n/a	288	4
1224.2.bx	$\chi_{1224}(625, \cdot)$	n/a	216	4
1224.2.bz	$\chi_{1224}(47, \cdot)$	None	0	4
1224.2.ca	$\chi_{1224}(659, \cdot)$	n/a	848	4
1224.2.cc	$\chi_{1224}(13, \cdot)$	n/a	848	4
1224.2.cf	$\chi_{1224}(233, \cdot)$	n/a	144	8
1224.2.cg	$\chi_{1224}(199, \cdot)$	None	0	8
1224.2.cj	$\chi_{1224}(91, \cdot)$	n/a	704	8
1224.2.ck	$\chi_{1224}(125, \cdot)$	n/a	576	8
1224.2.cm	$\chi_{1224}(229, \cdot)$	n/a	1696	8
1224.2.cn	$\chi_{1224}(59, \cdot)$	n/a	1696	8
1224.2.cs	$\chi_{1224}(25, \cdot)$	n/a	432	8
1224.2.ct	$\chi_{1224}(263, \cdot)$	None	0	8
1224.2.cv	$\chi_{1224}(7, \cdot)$	None	0	16
1224.2.cw	$\chi_{1224}(41, \cdot)$	n/a	864	16
1224.2.cz	$\chi_{1224}(5, \cdot)$	n/a	3392	16
1224.2.da	$\chi_{1224}(139, \cdot)$	n/a	3392	16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(1224))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(1224)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(136))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(153))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(204))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(306))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(408))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(612))$$^{\oplus 2}$