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

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