Space of modular forms of level 2736 and weight 2

• Label: 2736.2
• Level: 2736
• Weight: 2
• Dimension: 91139
• Nonzero newspaces: 64
• Sturm bound: 829440
• Trace bound: 33

Defining parameters

Level:	\( N \)	=	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 64 \)
Sturm bound:			\(829440\)
Trace bound:			\(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2736))\).

	Total	New	Old
Modular forms	211392	92515	118877
Cusp forms	203329	91139	112190
Eisenstein series	8063	1376	6687

Trace form

91139 * q - 96 * q^2 - 96 * q^3 - 100 * q^4 - 125 * q^5 - 128 * q^6 - 83 * q^7 - 108 * q^8 - 40 * q^9 - 292 * q^10 - 99 * q^11 - 128 * q^12 - 137 * q^13 - 60 * q^14 - 102 * q^15 - 52 * q^16 - 199 * q^17 - 88 * q^18 - 233 * q^19 - 104 * q^20 - 134 * q^21 - 4 * q^22 - 31 * q^23 - 64 * q^24 + 29 * q^25 + 20 * q^26 - 60 * q^27 - 212 * q^28 - 61 * q^29 - 88 * q^30 - 47 * q^31 - 36 * q^32 - 246 * q^33 - 76 * q^34 + 75 * q^35 - 120 * q^36 - 386 * q^37 - 148 * q^38 - 90 * q^39 - 212 * q^40 + 3 * q^41 - 208 * q^42 + 45 * q^43 - 268 * q^44 - 114 * q^45 - 412 * q^46 + 69 * q^47 - 232 * q^48 - 283 * q^49 - 264 * q^50 - 32 * q^51 - 220 * q^52 - 103 * q^53 - 216 * q^54 - 87 * q^55 - 300 * q^56 - 56 * q^57 - 280 * q^58 - 23 * q^59 - 344 * q^60 - 109 * q^61 - 300 * q^62 - 102 * q^63 - 148 * q^64 - 477 * q^65 - 368 * q^66 - 203 * q^67 - 268 * q^68 - 310 * q^69 - 20 * q^70 - 263 * q^71 - 352 * q^72 - 149 * q^73 - 212 * q^74 - 200 * q^75 - 68 * q^76 - 452 * q^77 - 344 * q^78 - 289 * q^79 - 364 * q^80 - 440 * q^81 - 308 * q^82 - 333 * q^83 - 416 * q^84 - 131 * q^85 - 388 * q^86 - 234 * q^87 - 244 * q^88 - 135 * q^89 - 416 * q^90 - 455 * q^91 - 292 * q^92 - 78 * q^93 - 292 * q^94 - 181 * q^95 - 408 * q^96 - 193 * q^97 - 280 * q^98 - 126 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2736))\)

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
2736.2.a	\(\chi_{2736}(1, \cdot)\)	2736.2.a.a	1	1
		2736.2.a.b	1
		2736.2.a.c	1
		2736.2.a.d	1
		2736.2.a.e	1
		2736.2.a.f	1
		2736.2.a.g	1
		2736.2.a.h	1
		2736.2.a.i	1
		2736.2.a.j	1
		2736.2.a.k	1
		2736.2.a.l	1
		2736.2.a.m	1
		2736.2.a.n	1
		2736.2.a.o	1
		2736.2.a.p	1
		2736.2.a.q	1
		2736.2.a.r	1
		2736.2.a.s	1
		2736.2.a.t	1
		2736.2.a.u	1
		2736.2.a.v	1
		2736.2.a.w	1
		2736.2.a.x	1
		2736.2.a.y	2
		2736.2.a.z	2
		2736.2.a.ba	2
		2736.2.a.bb	2
		2736.2.a.bc	3
		2736.2.a.bd	3
		2736.2.a.be	3
		2736.2.a.bf	4
2736.2.d	\(\chi_{2736}(2015, \cdot)\)	2736.2.d.a	12	1
		2736.2.d.b	24
2736.2.e	\(\chi_{2736}(1063, \cdot)\)	None	0	1
2736.2.f	\(\chi_{2736}(1025, \cdot)\)	2736.2.f.a	2	1
		2736.2.f.b	2
		2736.2.f.c	2
		2736.2.f.d	2
		2736.2.f.e	4
		2736.2.f.f	4
		2736.2.f.g	8
		2736.2.f.h	8
		2736.2.f.i	8
2736.2.g	\(\chi_{2736}(1369, \cdot)\)	None	0	1
2736.2.j	\(\chi_{2736}(647, \cdot)\)	None	0	1
2736.2.k	\(\chi_{2736}(2431, \cdot)\)	2736.2.k.a	2	1
		2736.2.k.b	2
		2736.2.k.c	2
		2736.2.k.d	2
		2736.2.k.e	2
		2736.2.k.f	2
		2736.2.k.g	2
		2736.2.k.h	2
		2736.2.k.i	2
		2736.2.k.j	4
		2736.2.k.k	4
		2736.2.k.l	4
		2736.2.k.m	4
		2736.2.k.n	4
		2736.2.k.o	4
		2736.2.k.p	8
2736.2.p	\(\chi_{2736}(2393, \cdot)\)	None	0	1
2736.2.q	\(\chi_{2736}(913, \cdot)\)	n/a	216	2
2736.2.r	\(\chi_{2736}(49, \cdot)\)	n/a	236	2
2736.2.s	\(\chi_{2736}(577, \cdot)\)	2736.2.s.a	2	2
		2736.2.s.b	2
		2736.2.s.c	2
		2736.2.s.d	2
		2736.2.s.e	2
		2736.2.s.f	2
		2736.2.s.g	2
		2736.2.s.h	2
		2736.2.s.i	2
		2736.2.s.j	2
		2736.2.s.k	2
		2736.2.s.l	2
		2736.2.s.m	2
		2736.2.s.n	2
		2736.2.s.o	2
		2736.2.s.p	2
		2736.2.s.q	2
		2736.2.s.r	2
		2736.2.s.s	4
		2736.2.s.t	4
		2736.2.s.u	4
		2736.2.s.v	4
		2736.2.s.w	4
		2736.2.s.x	6
		2736.2.s.y	6
		2736.2.s.z	6
		2736.2.s.ba	8
		2736.2.s.bb	8
		2736.2.s.bc	8
2736.2.t	\(\chi_{2736}(961, \cdot)\)	n/a	236	2
2736.2.u	\(\chi_{2736}(341, \cdot)\)	n/a	320	2
2736.2.x	\(\chi_{2736}(685, \cdot)\)	n/a	360	2
2736.2.y	\(\chi_{2736}(1331, \cdot)\)	n/a	288	2
2736.2.bb	\(\chi_{2736}(379, \cdot)\)	n/a	396	2
2736.2.be	\(\chi_{2736}(121, \cdot)\)	None	0	2
2736.2.bf	\(\chi_{2736}(65, \cdot)\)	n/a	236	2
2736.2.bg	\(\chi_{2736}(1015, \cdot)\)	None	0	2
2736.2.bh	\(\chi_{2736}(1679, \cdot)\)	n/a	240	2
2736.2.bm	\(\chi_{2736}(559, \cdot)\)	2736.2.bm.a	2	2
		2736.2.bm.b	2
		2736.2.bm.c	2
		2736.2.bm.d	2
		2736.2.bm.e	2
		2736.2.bm.f	2
		2736.2.bm.g	2
		2736.2.bm.h	2
		2736.2.bm.i	4
		2736.2.bm.j	4
		2736.2.bm.k	4
		2736.2.bm.l	6
		2736.2.bm.m	6
		2736.2.bm.n	6
		2736.2.bm.o	6
		2736.2.bm.p	8
		2736.2.bm.q	8
		2736.2.bm.r	8
		2736.2.bm.s	8
		2736.2.bm.t	16
2736.2.bn	\(\chi_{2736}(1223, \cdot)\)	None	0	2
2736.2.bq	\(\chi_{2736}(569, \cdot)\)	None	0	2
2736.2.bt	\(\chi_{2736}(2345, \cdot)\)	None	0	2
2736.2.bu	\(\chi_{2736}(943, \cdot)\)	n/a	240	2
2736.2.bv	\(\chi_{2736}(1607, \cdot)\)	None	0	2
2736.2.by	\(\chi_{2736}(1559, \cdot)\)	None	0	2
2736.2.bz	\(\chi_{2736}(607, \cdot)\)	n/a	240	2
2736.2.cc	\(\chi_{2736}(521, \cdot)\)	None	0	2
2736.2.cf	\(\chi_{2736}(487, \cdot)\)	None	0	2
2736.2.cg	\(\chi_{2736}(1151, \cdot)\)	2736.2.cg.a	24	2
		2736.2.cg.b	24
		2736.2.cg.c	32
2736.2.cj	\(\chi_{2736}(1033, \cdot)\)	None	0	2
2736.2.ck	\(\chi_{2736}(977, \cdot)\)	n/a	236	2
2736.2.cn	\(\chi_{2736}(113, \cdot)\)	n/a	236	2
2736.2.co	\(\chi_{2736}(457, \cdot)\)	None	0	2
2736.2.ct	\(\chi_{2736}(191, \cdot)\)	n/a	216	2
2736.2.cu	\(\chi_{2736}(151, \cdot)\)	None	0	2
2736.2.cx	\(\chi_{2736}(103, \cdot)\)	None	0	2
2736.2.cy	\(\chi_{2736}(239, \cdot)\)	n/a	240	2
2736.2.db	\(\chi_{2736}(505, \cdot)\)	None	0	2
2736.2.dc	\(\chi_{2736}(449, \cdot)\)	2736.2.dc.a	4	2
		2736.2.dc.b	4
		2736.2.dc.c	16
		2736.2.dc.d	16
		2736.2.dc.e	20
		2736.2.dc.f	20
2736.2.dd	\(\chi_{2736}(905, \cdot)\)	None	0	2
2736.2.di	\(\chi_{2736}(31, \cdot)\)	n/a	240	2
2736.2.dj	\(\chi_{2736}(311, \cdot)\)	None	0	2
2736.2.dk	\(\chi_{2736}(289, \cdot)\)	n/a	294	6
2736.2.dl	\(\chi_{2736}(625, \cdot)\)	n/a	708	6
2736.2.dm	\(\chi_{2736}(385, \cdot)\)	n/a	708	6
2736.2.do	\(\chi_{2736}(1189, \cdot)\)	n/a	792	4
2736.2.dp	\(\chi_{2736}(1133, \cdot)\)	n/a	640	4
2736.2.ds	\(\chi_{2736}(419, \cdot)\)	n/a	1728	4
2736.2.dt	\(\chi_{2736}(331, \cdot)\)	n/a	1904	4
2736.2.dv	\(\chi_{2736}(259, \cdot)\)	n/a	1904	4
2736.2.dy	\(\chi_{2736}(83, \cdot)\)	n/a	1904	4
2736.2.ea	\(\chi_{2736}(11, \cdot)\)	n/a	1904	4
2736.2.eb	\(\chi_{2736}(835, \cdot)\)	n/a	1904	4
2736.2.ee	\(\chi_{2736}(797, \cdot)\)	n/a	1904	4
2736.2.ef	\(\chi_{2736}(349, \cdot)\)	n/a	1904	4
2736.2.eh	\(\chi_{2736}(277, \cdot)\)	n/a	1904	4
2736.2.ek	\(\chi_{2736}(221, \cdot)\)	n/a	1904	4
2736.2.em	\(\chi_{2736}(293, \cdot)\)	n/a	1904	4
2736.2.en	\(\chi_{2736}(229, \cdot)\)	n/a	1728	4
2736.2.eq	\(\chi_{2736}(1171, \cdot)\)	n/a	792	4
2736.2.er	\(\chi_{2736}(467, \cdot)\)	n/a	640	4
2736.2.eu	\(\chi_{2736}(439, \cdot)\)	None	0	6
2736.2.ew	\(\chi_{2736}(671, \cdot)\)	n/a	720	6
2736.2.ex	\(\chi_{2736}(79, \cdot)\)	n/a	720	6
2736.2.ez	\(\chi_{2736}(23, \cdot)\)	None	0	6
2736.2.fb	\(\chi_{2736}(401, \cdot)\)	n/a	708	6
2736.2.fd	\(\chi_{2736}(25, \cdot)\)	None	0	6
2736.2.fh	\(\chi_{2736}(89, \cdot)\)	None	0	6
2736.2.fi	\(\chi_{2736}(73, \cdot)\)	None	0	6
2736.2.fk	\(\chi_{2736}(737, \cdot)\)	n/a	240	6
2736.2.fn	\(\chi_{2736}(41, \cdot)\)	None	0	6
2736.2.fp	\(\chi_{2736}(1031, \cdot)\)	None	0	6
2736.2.fr	\(\chi_{2736}(895, \cdot)\)	n/a	720	6
2736.2.fu	\(\chi_{2736}(775, \cdot)\)	None	0	6
2736.2.fw	\(\chi_{2736}(575, \cdot)\)	n/a	240	6
2736.2.fx	\(\chi_{2736}(127, \cdot)\)	n/a	300	6
2736.2.fz	\(\chi_{2736}(215, \cdot)\)	None	0	6
2736.2.gc	\(\chi_{2736}(47, \cdot)\)	n/a	720	6
2736.2.ge	\(\chi_{2736}(295, \cdot)\)	None	0	6
2736.2.gh	\(\chi_{2736}(857, \cdot)\)	None	0	6
2736.2.gi	\(\chi_{2736}(169, \cdot)\)	None	0	6
2736.2.gk	\(\chi_{2736}(257, \cdot)\)	n/a	708	6
2736.2.gm	\(\chi_{2736}(85, \cdot)\)	n/a	5712	12
2736.2.go	\(\chi_{2736}(173, \cdot)\)	n/a	5712	12
2736.2.gq	\(\chi_{2736}(131, \cdot)\)	n/a	5712	12
2736.2.gt	\(\chi_{2736}(91, \cdot)\)	n/a	2376	12
2736.2.gv	\(\chi_{2736}(35, \cdot)\)	n/a	1920	12
2736.2.gw	\(\chi_{2736}(211, \cdot)\)	n/a	5712	12
2736.2.gz	\(\chi_{2736}(29, \cdot)\)	n/a	5712	12
2736.2.ha	\(\chi_{2736}(253, \cdot)\)	n/a	2376	12
2736.2.hc	\(\chi_{2736}(53, \cdot)\)	n/a	1920	12
2736.2.hf	\(\chi_{2736}(61, \cdot)\)	n/a	5712	12
2736.2.hh	\(\chi_{2736}(67, \cdot)\)	n/a	5712	12
2736.2.hj	\(\chi_{2736}(275, \cdot)\)	n/a	5712	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2736))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2736)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1368))\)\(^{\oplus 2}\)