Space of modular forms of level 2664 and weight 2

• Label: 2664.2
• Level: 2664
• Weight: 2
• Dimension: 86965
• Nonzero newspaces: 72
• Sturm bound: 787968
• Trace bound: 47

Defining parameters

Level:	\( N \)	=	\( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 72 \)
Sturm bound:			\(787968\)
Trace bound:			\(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2664))\).

	Total	New	Old
Modular forms	200448	88225	112223
Cusp forms	193537	86965	106572
Eisenstein series	6911	1260	5651

Trace form

86965 * q - 104 * q^2 - 138 * q^3 - 104 * q^4 - 8 * q^5 - 128 * q^6 - 104 * q^7 - 80 * q^8 - 270 * q^9 - 276 * q^10 - 74 * q^11 - 116 * q^12 + 4 * q^13 - 80 * q^14 - 96 * q^15 - 88 * q^16 - 176 * q^17 - 144 * q^18 - 280 * q^19 - 128 * q^20 + 24 * q^21 - 136 * q^22 - 72 * q^23 - 192 * q^24 - 200 * q^25 - 164 * q^26 - 144 * q^27 - 340 * q^28 - 12 * q^29 - 236 * q^30 - 76 * q^31 - 184 * q^32 - 274 * q^33 - 80 * q^34 - 180 * q^35 - 244 * q^36 - 6 * q^37 - 292 * q^38 - 216 * q^39 - 128 * q^40 - 206 * q^41 - 244 * q^42 - 158 * q^43 - 192 * q^44 - 4 * q^45 - 356 * q^46 - 192 * q^47 - 184 * q^48 - 112 * q^49 - 164 * q^50 - 162 * q^51 - 56 * q^52 + 28 * q^53 - 120 * q^54 - 292 * q^55 - 44 * q^56 - 230 * q^57 - 88 * q^58 - 146 * q^59 - 12 * q^60 - 29 * q^61 + 20 * q^62 - 208 * q^63 - 284 * q^64 - 229 * q^65 + 64 * q^66 - 94 * q^67 + 60 * q^68 - 44 * q^69 - 16 * q^70 - 196 * q^71 + 60 * q^72 - 672 * q^73 + 2 * q^74 - 386 * q^75 - 40 * q^76 - 96 * q^77 + 4 * q^78 - 172 * q^79 + 84 * q^80 - 310 * q^81 - 364 * q^82 - 208 * q^83 - 16 * q^84 - 97 * q^85 - 8 * q^86 - 180 * q^87 - 136 * q^88 - 305 * q^89 - 116 * q^90 - 408 * q^91 - 216 * q^92 + 20 * q^93 - 156 * q^94 - 236 * q^95 - 240 * q^96 - 318 * q^97 - 300 * q^98 - 204 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2664))\)

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
2664.2.a	\(\chi_{2664}(1, \cdot)\)	2664.2.a.a	1	1
		2664.2.a.b	1
		2664.2.a.c	1
		2664.2.a.d	1
		2664.2.a.e	1
		2664.2.a.f	1
		2664.2.a.g	1
		2664.2.a.h	1
		2664.2.a.i	2
		2664.2.a.j	2
		2664.2.a.k	2
		2664.2.a.l	2
		2664.2.a.m	3
		2664.2.a.n	3
		2664.2.a.o	3
		2664.2.a.p	3
		2664.2.a.q	3
		2664.2.a.r	4
		2664.2.a.s	5
		2664.2.a.t	5
2664.2.c	\(\chi_{2664}(1331, \cdot)\)	n/a	152	1
2664.2.e	\(\chi_{2664}(2591, \cdot)\)	None	0	1
2664.2.f	\(\chi_{2664}(1333, \cdot)\)	n/a	180	1
2664.2.h	\(\chi_{2664}(73, \cdot)\)	2664.2.h.a	2	1
		2664.2.h.b	6
		2664.2.h.c	10
		2664.2.h.d	10
		2664.2.h.e	20
2664.2.j	\(\chi_{2664}(1259, \cdot)\)	n/a	144	1
2664.2.l	\(\chi_{2664}(2663, \cdot)\)	None	0	1
2664.2.o	\(\chi_{2664}(1405, \cdot)\)	n/a	188	1
2664.2.q	\(\chi_{2664}(889, \cdot)\)	n/a	216	2
2664.2.r	\(\chi_{2664}(433, \cdot)\)	2664.2.r.a	2	2
		2664.2.r.b	2
		2664.2.r.c	2
		2664.2.r.d	2
		2664.2.r.e	2
		2664.2.r.f	2
		2664.2.r.g	2
		2664.2.r.h	6
		2664.2.r.i	6
		2664.2.r.j	6
		2664.2.r.k	6
		2664.2.r.l	6
		2664.2.r.m	8
		2664.2.r.n	10
		2664.2.r.o	16
		2664.2.r.p	16
2664.2.s	\(\chi_{2664}(1897, \cdot)\)	n/a	228	2
2664.2.t	\(\chi_{2664}(121, \cdot)\)	n/a	228	2
2664.2.u	\(\chi_{2664}(1819, \cdot)\)	n/a	376	2
2664.2.w	\(\chi_{2664}(487, \cdot)\)	None	0	2
2664.2.z	\(\chi_{2664}(413, \cdot)\)	n/a	304	2
2664.2.bb	\(\chi_{2664}(1745, \cdot)\)	2664.2.bb.a	36	2
		2664.2.bb.b	40
2664.2.bc	\(\chi_{2664}(529, \cdot)\)	n/a	228	2
2664.2.be	\(\chi_{2664}(1453, \cdot)\)	n/a	904	2
2664.2.bh	\(\chi_{2664}(1823, \cdot)\)	None	0	2
2664.2.bj	\(\chi_{2664}(11, \cdot)\)	n/a	904	2
2664.2.bl	\(\chi_{2664}(455, \cdot)\)	None	0	2
2664.2.bn	\(\chi_{2664}(1379, \cdot)\)	n/a	904	2
2664.2.bo	\(\chi_{2664}(397, \cdot)\)	n/a	376	2
2664.2.br	\(\chi_{2664}(517, \cdot)\)	n/a	904	2
2664.2.bv	\(\chi_{2664}(1691, \cdot)\)	n/a	304	2
2664.2.bx	\(\chi_{2664}(887, \cdot)\)	None	0	2
2664.2.bz	\(\chi_{2664}(371, \cdot)\)	n/a	864	2
2664.2.cb	\(\chi_{2664}(1655, \cdot)\)	None	0	2
2664.2.cd	\(\chi_{2664}(85, \cdot)\)	n/a	904	2
2664.2.cf	\(\chi_{2664}(47, \cdot)\)	None	0	2
2664.2.ch	\(\chi_{2664}(1787, \cdot)\)	n/a	904	2
2664.2.ck	\(\chi_{2664}(1765, \cdot)\)	n/a	376	2
2664.2.cm	\(\chi_{2664}(961, \cdot)\)	n/a	228	2
2664.2.co	\(\chi_{2664}(445, \cdot)\)	n/a	864	2
2664.2.cq	\(\chi_{2664}(1729, \cdot)\)	2664.2.cq.a	8	2
		2664.2.cq.b	8
		2664.2.cq.c	20
		2664.2.cq.d	20
		2664.2.cq.e	40
2664.2.cr	\(\chi_{2664}(323, \cdot)\)	n/a	304	2
2664.2.ct	\(\chi_{2664}(815, \cdot)\)	None	0	2
2664.2.cv	\(\chi_{2664}(443, \cdot)\)	n/a	904	2
2664.2.cx	\(\chi_{2664}(359, \cdot)\)	None	0	2
2664.2.da	\(\chi_{2664}(1417, \cdot)\)	n/a	228	2
2664.2.dc	\(\chi_{2664}(565, \cdot)\)	n/a	904	2
2664.2.df	\(\chi_{2664}(1861, \cdot)\)	n/a	904	2
2664.2.dg	\(\chi_{2664}(1343, \cdot)\)	None	0	2
2664.2.di	\(\chi_{2664}(491, \cdot)\)	n/a	904	2
2664.2.dk	\(\chi_{2664}(49, \cdot)\)	n/a	684	6
2664.2.dl	\(\chi_{2664}(145, \cdot)\)	n/a	282	6
2664.2.dm	\(\chi_{2664}(601, \cdot)\)	n/a	684	6
2664.2.do	\(\chi_{2664}(103, \cdot)\)	None	0	4
2664.2.dq	\(\chi_{2664}(763, \cdot)\)	n/a	1808	4
2664.2.dr	\(\chi_{2664}(125, \cdot)\)	n/a	608	4
2664.2.du	\(\chi_{2664}(689, \cdot)\)	n/a	456	4
2664.2.dv	\(\chi_{2664}(401, \cdot)\)	n/a	456	4
2664.2.dy	\(\chi_{2664}(29, \cdot)\)	n/a	1808	4
2664.2.dz	\(\chi_{2664}(1301, \cdot)\)	n/a	1808	4
2664.2.eb	\(\chi_{2664}(1457, \cdot)\)	n/a	152	4
2664.2.ee	\(\chi_{2664}(1531, \cdot)\)	n/a	752	4
2664.2.ef	\(\chi_{2664}(319, \cdot)\)	None	0	4
2664.2.ei	\(\chi_{2664}(31, \cdot)\)	None	0	4
2664.2.ej	\(\chi_{2664}(547, \cdot)\)	n/a	1808	4
2664.2.em	\(\chi_{2664}(43, \cdot)\)	n/a	1808	4
2664.2.eo	\(\chi_{2664}(199, \cdot)\)	None	0	4
2664.2.ep	\(\chi_{2664}(473, \cdot)\)	n/a	456	4
2664.2.er	\(\chi_{2664}(245, \cdot)\)	n/a	1808	4
2664.2.eu	\(\chi_{2664}(707, \cdot)\)	n/a	2712	6
2664.2.ev	\(\chi_{2664}(373, \cdot)\)	n/a	2712	6
2664.2.ey	\(\chi_{2664}(229, \cdot)\)	n/a	2712	6
2664.2.ez	\(\chi_{2664}(83, \cdot)\)	n/a	2712	6
2664.2.fd	\(\chi_{2664}(71, \cdot)\)	None	0	6
2664.2.fg	\(\chi_{2664}(527, \cdot)\)	None	0	6
2664.2.fh	\(\chi_{2664}(95, \cdot)\)	None	0	6
2664.2.fk	\(\chi_{2664}(215, \cdot)\)	None	0	6
2664.2.fl	\(\chi_{2664}(289, \cdot)\)	n/a	288	6
2664.2.fo	\(\chi_{2664}(817, \cdot)\)	n/a	684	6
2664.2.fq	\(\chi_{2664}(107, \cdot)\)	n/a	912	6
2664.2.fr	\(\chi_{2664}(155, \cdot)\)	n/a	2712	6
2664.2.fu	\(\chi_{2664}(157, \cdot)\)	n/a	2712	6
2664.2.fv	\(\chi_{2664}(181, \cdot)\)	n/a	1128	6
2664.2.fy	\(\chi_{2664}(469, \cdot)\)	n/a	1128	6
2664.2.fz	\(\chi_{2664}(781, \cdot)\)	n/a	2712	6
2664.2.gc	\(\chi_{2664}(299, \cdot)\)	n/a	2712	6
2664.2.gd	\(\chi_{2664}(395, \cdot)\)	n/a	912	6
2664.2.gg	\(\chi_{2664}(25, \cdot)\)	n/a	684	6
2664.2.gh	\(\chi_{2664}(743, \cdot)\)	None	0	6
2664.2.gk	\(\chi_{2664}(599, \cdot)\)	None	0	6
2664.2.go	\(\chi_{2664}(187, \cdot)\)	n/a	5424	12
2664.2.gp	\(\chi_{2664}(5, \cdot)\)	n/a	5424	12
2664.2.gq	\(\chi_{2664}(79, \cdot)\)	None	0	12
2664.2.gr	\(\chi_{2664}(113, \cdot)\)	n/a	1368	12
2664.2.gu	\(\chi_{2664}(17, \cdot)\)	n/a	456	12
2664.2.gv	\(\chi_{2664}(55, \cdot)\)	None	0	12
2664.2.gy	\(\chi_{2664}(389, \cdot)\)	n/a	5424	12
2664.2.gz	\(\chi_{2664}(355, \cdot)\)	n/a	5424	12
2664.2.hc	\(\chi_{2664}(19, \cdot)\)	n/a	2256	12
2664.2.hd	\(\chi_{2664}(557, \cdot)\)	n/a	1824	12
2664.2.hi	\(\chi_{2664}(281, \cdot)\)	n/a	1368	12
2664.2.hj	\(\chi_{2664}(463, \cdot)\)	None	0	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2664)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(666))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1332))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2664))\)\(^{\oplus 1}\)