Space of modular forms of level 3264 and weight 2

• Label: 3264.2
• Level: 3264
• Weight: 2
• Dimension: 122892
• Nonzero newspaces: 68
• Sturm bound: 1179648
• Trace bound: 65

Defining parameters

Level:	$N$	=	$3264 = 2^{6} \cdot 3 \cdot 17$
Weight:	$k$	=	$2$
Nonzero newspaces:			$68$
Sturm bound:			$1179648$
Trace bound:			$65$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(3264))$.

	Total	New	Old
Modular forms	299520	124212	175308
Cusp forms	290305	122892	167413
Eisenstein series	9215	1320	7895

Trace form

122892 * q - 84 * q^3 - 224 * q^4 - 112 * q^6 - 176 * q^7 - 140 * q^9 - 224 * q^10 - 16 * q^11 - 112 * q^12 - 256 * q^13 - 96 * q^15 - 224 * q^16 - 16 * q^17 - 240 * q^18 - 200 * q^19 - 104 * q^21 - 192 * q^22 - 32 * q^24 - 236 * q^25 + 160 * q^26 - 60 * q^27 - 64 * q^28 + 64 * q^29 + 48 * q^30 - 80 * q^31 + 160 * q^32 - 8 * q^33 - 160 * q^34 + 48 * q^35 + 48 * q^36 - 160 * q^37 + 160 * q^38 - 40 * q^39 - 64 * q^40 + 64 * q^41 - 32 * q^42 - 152 * q^43 + 32 * q^44 - 24 * q^45 - 224 * q^46 - 112 * q^48 - 364 * q^49 - 96 * q^50 - 24 * q^51 - 672 * q^52 - 144 * q^54 + 144 * q^55 - 224 * q^56 - 88 * q^57 - 512 * q^58 + 320 * q^59 - 304 * q^60 - 224 * q^61 - 192 * q^62 - 16 * q^63 - 608 * q^64 + 32 * q^65 - 272 * q^66 + 184 * q^67 - 96 * q^68 - 312 * q^69 - 608 * q^70 + 256 * q^71 - 112 * q^72 - 280 * q^73 - 224 * q^74 + 12 * q^75 - 480 * q^76 - 96 * q^77 - 256 * q^78 - 80 * q^79 - 96 * q^80 - 324 * q^81 - 224 * q^82 - 80 * q^83 - 336 * q^84 - 288 * q^85 - 200 * q^87 - 224 * q^88 - 64 * q^89 - 400 * q^90 - 288 * q^91 - 224 * q^93 - 224 * q^94 - 96 * q^95 - 384 * q^96 - 264 * q^97 - 200 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(3264))$

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
3264.2.a	$\chi_{3264}(1, \cdot)$	3264.2.a.a	1	1
		3264.2.a.b	1
		3264.2.a.c	1
		3264.2.a.d	1
		3264.2.a.e	1
		3264.2.a.f	1
		3264.2.a.g	1
		3264.2.a.h	1
		3264.2.a.i	1
		3264.2.a.j	1
		3264.2.a.k	1
		3264.2.a.l	1
		3264.2.a.m	1
		3264.2.a.n	1
		3264.2.a.o	1
		3264.2.a.p	1
		3264.2.a.q	1
		3264.2.a.r	1
		3264.2.a.s	1
		3264.2.a.t	1
		3264.2.a.u	1
		3264.2.a.v	1
		3264.2.a.w	1
		3264.2.a.x	1
		3264.2.a.y	1
		3264.2.a.z	1
		3264.2.a.ba	1
		3264.2.a.bb	1
		3264.2.a.bc	1
		3264.2.a.bd	1
		3264.2.a.be	1
		3264.2.a.bf	1
		3264.2.a.bg	2
		3264.2.a.bh	2
		3264.2.a.bi	2
		3264.2.a.bj	2
		3264.2.a.bk	2
		3264.2.a.bl	2
		3264.2.a.bm	2
		3264.2.a.bn	2
		3264.2.a.bo	2
		3264.2.a.bp	2
		3264.2.a.bq	3
		3264.2.a.br	3
		3264.2.a.bs	3
		3264.2.a.bt	3
3264.2.c	$\chi_{3264}(577, \cdot)$	3264.2.c.a	2	1
		3264.2.c.b	2
		3264.2.c.c	2
		3264.2.c.d	2
		3264.2.c.e	2
		3264.2.c.f	2
		3264.2.c.g	2
		3264.2.c.h	2
		3264.2.c.i	2
		3264.2.c.j	2
		3264.2.c.k	4
		3264.2.c.l	4
		3264.2.c.m	4
		3264.2.c.n	6
		3264.2.c.o	6
		3264.2.c.p	8
		3264.2.c.q	10
		3264.2.c.r	10
3264.2.e	$\chi_{3264}(2687, \cdot)$	n/a	128	1
3264.2.f	$\chi_{3264}(1633, \cdot)$	3264.2.f.a	2	1
		3264.2.f.b	2
		3264.2.f.c	4
		3264.2.f.d	4
		3264.2.f.e	4
		3264.2.f.f	8
		3264.2.f.g	8
		3264.2.f.h	8
		3264.2.f.i	8
		3264.2.f.j	16
3264.2.h	$\chi_{3264}(1631, \cdot)$	n/a	144	1
3264.2.j	$\chi_{3264}(1055, \cdot)$	n/a	128	1
3264.2.l	$\chi_{3264}(2209, \cdot)$	3264.2.l.a	4	1
		3264.2.l.b	4
		3264.2.l.c	8
		3264.2.l.d	8
		3264.2.l.e	24
		3264.2.l.f	24
3264.2.o	$\chi_{3264}(3263, \cdot)$	n/a	140	1
3264.2.r	$\chi_{3264}(47, \cdot)$	n/a	280	2
3264.2.s	$\chi_{3264}(625, \cdot)$	n/a	144	2
3264.2.u	$\chi_{3264}(817, \cdot)$	n/a	128	2
3264.2.w	$\chi_{3264}(815, \cdot)$	n/a	280	2
3264.2.y	$\chi_{3264}(863, \cdot)$	n/a	288	2
3264.2.ba	$\chi_{3264}(1441, \cdot)$	n/a	144	2
3264.2.bd	$\chi_{3264}(769, \cdot)$	n/a	144	2
3264.2.bf	$\chi_{3264}(191, \cdot)$	n/a	280	2
3264.2.bh	$\chi_{3264}(239, \cdot)$	n/a	256	2
3264.2.bj	$\chi_{3264}(1393, \cdot)$	n/a	144	2
3264.2.bl	$\chi_{3264}(1585, \cdot)$	n/a	144	2
3264.2.bm	$\chi_{3264}(1007, \cdot)$	n/a	280	2
3264.2.bp	$\chi_{3264}(1511, \cdot)$	None	0	4
3264.2.br	$\chi_{3264}(553, \cdot)$	None	0	4
3264.2.bt	$\chi_{3264}(455, \cdot)$	None	0	4
3264.2.bv	$\chi_{3264}(1033, \cdot)$	None	0	4
3264.2.bx	$\chi_{3264}(263, \cdot)$	None	0	4
3264.2.bz	$\chi_{3264}(457, \cdot)$	None	0	4
3264.2.cc	$\chi_{3264}(961, \cdot)$	n/a	288	4
3264.2.cd	$\chi_{3264}(383, \cdot)$	n/a	560	4
3264.2.ce	$\chi_{3264}(1103, \cdot)$	n/a	560	4
3264.2.cf	$\chi_{3264}(433, \cdot)$	n/a	288	4
3264.2.ci	$\chi_{3264}(169, \cdot)$	None	0	4
3264.2.cj	$\chi_{3264}(647, \cdot)$	None	0	4
3264.2.cm	$\chi_{3264}(407, \cdot)$	None	0	4
3264.2.cn	$\chi_{3264}(409, \cdot)$	None	0	4
3264.2.cq	$\chi_{3264}(1487, \cdot)$	n/a	560	4
3264.2.cr	$\chi_{3264}(49, \cdot)$	n/a	288	4
3264.2.cu	$\chi_{3264}(865, \cdot)$	n/a	288	4
3264.2.cv	$\chi_{3264}(287, \cdot)$	n/a	576	4
3264.2.cz	$\chi_{3264}(25, \cdot)$	None	0	4
3264.2.db	$\chi_{3264}(1607, \cdot)$	None	0	4
3264.2.dc	$\chi_{3264}(217, \cdot)$	None	0	4
3264.2.de	$\chi_{3264}(1271, \cdot)$	None	0	4
3264.2.dh	$\chi_{3264}(121, \cdot)$	None	0	4
3264.2.dj	$\chi_{3264}(359, \cdot)$	None	0	4
3264.2.dm	$\chi_{3264}(197, \cdot)$	n/a	4576	8
3264.2.dn	$\chi_{3264}(403, \cdot)$	n/a	2304	8
3264.2.do	$\chi_{3264}(229, \cdot)$	n/a	2304	8
3264.2.dq	$\chi_{3264}(563, \cdot)$	n/a	4576	8
3264.2.ds	$\chi_{3264}(139, \cdot)$	n/a	2304	8
3264.2.dt	$\chi_{3264}(317, \cdot)$	n/a	4576	8
3264.2.dx	$\chi_{3264}(113, \cdot)$	n/a	1120	8
3264.2.dy	$\chi_{3264}(79, \cdot)$	n/a	576	8
3264.2.eb	$\chi_{3264}(7, \cdot)$	None	0	8
3264.2.ec	$\chi_{3264}(233, \cdot)$	None	0	8
3264.2.ee	$\chi_{3264}(467, \cdot)$	n/a	4576	8
3264.2.eg	$\chi_{3264}(349, \cdot)$	n/a	2304	8
3264.2.ek	$\chi_{3264}(245, \cdot)$	n/a	4576	8
3264.2.el	$\chi_{3264}(283, \cdot)$	n/a	2304	8
3264.2.eo	$\chi_{3264}(29, \cdot)$	n/a	4576	8
3264.2.ep	$\chi_{3264}(91, \cdot)$	n/a	2304	8
3264.2.eq	$\chi_{3264}(499, \cdot)$	n/a	2304	8
3264.2.er	$\chi_{3264}(437, \cdot)$	n/a	4576	8
3264.2.ew	$\chi_{3264}(205, \cdot)$	n/a	2048	8
3264.2.ex	$\chi_{3264}(203, \cdot)$	n/a	4576	8
3264.2.ez	$\chi_{3264}(65, \cdot)$	n/a	1120	8
3264.2.fa	$\chi_{3264}(703, \cdot)$	n/a	576	8
3264.2.fc	$\chi_{3264}(41, \cdot)$	None	0	8
3264.2.ff	$\chi_{3264}(199, \cdot)$	None	0	8
3264.2.fg	$\chi_{3264}(13, \cdot)$	n/a	2304	8
3264.2.fh	$\chi_{3264}(251, \cdot)$	n/a	4576	8
3264.2.fm	$\chi_{3264}(157, \cdot)$	n/a	2304	8
3264.2.fn	$\chi_{3264}(395, \cdot)$	n/a	4576	8
3264.2.fo	$\chi_{3264}(473, \cdot)$	None	0	8
3264.2.fr	$\chi_{3264}(1159, \cdot)$	None	0	8
3264.2.ft	$\chi_{3264}(31, \cdot)$	n/a	576	8
3264.2.fu	$\chi_{3264}(737, \cdot)$	n/a	1152	8
3264.2.fw	$\chi_{3264}(35, \cdot)$	n/a	4096	8
3264.2.fx	$\chi_{3264}(373, \cdot)$	n/a	2304	8
3264.2.ga	$\chi_{3264}(581, \cdot)$	n/a	4576	8
3264.2.gb	$\chi_{3264}(163, \cdot)$	n/a	2304	8
3264.2.ge	$\chi_{3264}(325, \cdot)$	n/a	2304	8
3264.2.gg	$\chi_{3264}(155, \cdot)$	n/a	4576	8
3264.2.gi	$\chi_{3264}(439, \cdot)$	None	0	8
3264.2.gl	$\chi_{3264}(1193, \cdot)$	None	0	8
3264.2.gn	$\chi_{3264}(401, \cdot)$	n/a	1120	8
3264.2.go	$\chi_{3264}(367, \cdot)$	n/a	576	8
3264.2.gq	$\chi_{3264}(379, \cdot)$	n/a	2304	8
3264.2.gr	$\chi_{3264}(5, \cdot)$	n/a	4576	8
3264.2.gu	$\chi_{3264}(59, \cdot)$	n/a	4576	8
3264.2.gw	$\chi_{3264}(253, \cdot)$	n/a	2304	8
3264.2.ha	$\chi_{3264}(547, \cdot)$	n/a	2304	8
3264.2.hb	$\chi_{3264}(533, \cdot)$	n/a	4576	8

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(3264))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(3264)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 28}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$^{\oplus 7}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(136))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(204))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(272))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(408))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(544))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(816))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1088))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1632))$$^{\oplus 2}$