Space of modular forms of level 3648 and weight 2

• Label: 3648.2
• Level: 3648
• Weight: 2
• Dimension: 153908
• Nonzero newspaces: 48
• Sturm bound: 1474560
• Trace bound: 51

Defining parameters

Level:	\( N \)	=	\( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(1474560\)
Trace bound:			\(51\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3648))\).

	Total	New	Old
Modular forms	373824	155404	218420
Cusp forms	363457	153908	209549
Eisenstein series	10367	1496	8871

Trace form

153908 * q - 96 * q^3 - 256 * q^4 - 128 * q^6 - 200 * q^7 - 160 * q^9 - 256 * q^10 - 16 * q^11 - 128 * q^12 - 288 * q^13 - 108 * q^15 - 256 * q^16 - 32 * q^17 - 128 * q^18 - 220 * q^19 - 120 * q^21 - 224 * q^22 - 48 * q^24 - 276 * q^25 + 160 * q^26 - 72 * q^27 - 96 * q^28 + 64 * q^29 + 32 * q^30 - 104 * q^31 + 160 * q^32 - 20 * q^33 - 96 * q^34 + 48 * q^35 + 32 * q^36 - 192 * q^37 + 80 * q^38 - 160 * q^39 - 96 * q^40 + 64 * q^41 - 48 * q^42 - 176 * q^43 + 32 * q^44 - 40 * q^45 - 256 * q^46 - 128 * q^48 - 420 * q^49 - 96 * q^50 + 36 * q^51 - 448 * q^52 - 160 * q^54 + 120 * q^55 - 224 * q^56 - 144 * q^57 - 832 * q^58 + 320 * q^59 - 320 * q^60 - 256 * q^61 - 192 * q^62 - 28 * q^63 - 640 * q^64 + 32 * q^65 - 288 * q^66 + 160 * q^67 - 192 * q^68 - 200 * q^69 - 640 * q^70 + 256 * q^71 - 128 * q^72 - 320 * q^73 - 224 * q^74 - 400 * q^76 - 96 * q^77 - 272 * q^78 - 104 * q^79 - 96 * q^80 - 352 * q^81 - 256 * q^82 - 80 * q^83 - 352 * q^84 - 352 * q^85 - 212 * q^87 - 256 * q^88 - 64 * q^89 - 416 * q^90 - 312 * q^91 - 240 * q^93 - 256 * q^94 - 48 * q^95 - 544 * q^96 - 288 * q^97 - 212 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3648))\)

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
3648.2.a	\(\chi_{3648}(1, \cdot)\)	3648.2.a.a	1	1
		3648.2.a.b	1
		3648.2.a.c	1
		3648.2.a.d	1
		3648.2.a.e	1
		3648.2.a.f	1
		3648.2.a.g	1
		3648.2.a.h	1
		3648.2.a.i	1
		3648.2.a.j	1
		3648.2.a.k	1
		3648.2.a.l	1
		3648.2.a.m	1
		3648.2.a.n	1
		3648.2.a.o	1
		3648.2.a.p	1
		3648.2.a.q	1
		3648.2.a.r	1
		3648.2.a.s	1
		3648.2.a.t	1
		3648.2.a.u	1
		3648.2.a.v	1
		3648.2.a.w	1
		3648.2.a.x	1
		3648.2.a.y	1
		3648.2.a.z	1
		3648.2.a.ba	1
		3648.2.a.bb	1
		3648.2.a.bc	1
		3648.2.a.bd	1
		3648.2.a.be	1
		3648.2.a.bf	1
		3648.2.a.bg	1
		3648.2.a.bh	1
		3648.2.a.bi	1
		3648.2.a.bj	1
		3648.2.a.bk	2
		3648.2.a.bl	2
		3648.2.a.bm	2
		3648.2.a.bn	2
		3648.2.a.bo	2
		3648.2.a.bp	2
		3648.2.a.bq	2
		3648.2.a.br	2
		3648.2.a.bs	2
		3648.2.a.bt	2
		3648.2.a.bu	2
		3648.2.a.bv	2
		3648.2.a.bw	3
		3648.2.a.bx	3
		3648.2.a.by	3
		3648.2.a.bz	3
3648.2.d	\(\chi_{3648}(191, \cdot)\)	n/a	144	1
3648.2.e	\(\chi_{3648}(607, \cdot)\)	3648.2.e.a	12	1
		3648.2.e.b	12
		3648.2.e.c	28
		3648.2.e.d	28
3648.2.f	\(\chi_{3648}(1025, \cdot)\)	n/a	156	1
3648.2.g	\(\chi_{3648}(1825, \cdot)\)	3648.2.g.a	4	1
		3648.2.g.b	4
		3648.2.g.c	4
		3648.2.g.d	4
		3648.2.g.e	4
		3648.2.g.f	8
		3648.2.g.g	8
		3648.2.g.h	8
		3648.2.g.i	12
		3648.2.g.j	16
3648.2.j	\(\chi_{3648}(2015, \cdot)\)	n/a	144	1
3648.2.k	\(\chi_{3648}(2431, \cdot)\)	3648.2.k.a	2	1
		3648.2.k.b	2
		3648.2.k.c	2
		3648.2.k.d	2
		3648.2.k.e	2
		3648.2.k.f	2
		3648.2.k.g	4
		3648.2.k.h	4
		3648.2.k.i	10
		3648.2.k.j	10
		3648.2.k.k	20
		3648.2.k.l	20
3648.2.p	\(\chi_{3648}(2849, \cdot)\)	n/a	160	1
3648.2.q	\(\chi_{3648}(577, \cdot)\)	n/a	160	2
3648.2.r	\(\chi_{3648}(113, \cdot)\)	n/a	312	2
3648.2.u	\(\chi_{3648}(913, \cdot)\)	n/a	144	2
3648.2.v	\(\chi_{3648}(1103, \cdot)\)	n/a	288	2
3648.2.y	\(\chi_{3648}(1519, \cdot)\)	n/a	160	2
3648.2.bb	\(\chi_{3648}(1471, \cdot)\)	n/a	160	2
3648.2.bc	\(\chi_{3648}(2591, \cdot)\)	n/a	320	2
3648.2.bd	\(\chi_{3648}(1889, \cdot)\)	n/a	320	2
3648.2.bg	\(\chi_{3648}(31, \cdot)\)	n/a	160	2
3648.2.bh	\(\chi_{3648}(767, \cdot)\)	n/a	312	2
3648.2.bm	\(\chi_{3648}(2401, \cdot)\)	n/a	160	2
3648.2.bn	\(\chi_{3648}(65, \cdot)\)	n/a	312	2
3648.2.bq	\(\chi_{3648}(457, \cdot)\)	None	0	4
3648.2.br	\(\chi_{3648}(151, \cdot)\)	None	0	4
3648.2.bs	\(\chi_{3648}(647, \cdot)\)	None	0	4
3648.2.bt	\(\chi_{3648}(569, \cdot)\)	None	0	4
3648.2.bw	\(\chi_{3648}(385, \cdot)\)	n/a	480	6
3648.2.by	\(\chi_{3648}(49, \cdot)\)	n/a	320	4
3648.2.bz	\(\chi_{3648}(977, \cdot)\)	n/a	624	4
3648.2.cc	\(\chi_{3648}(559, \cdot)\)	n/a	320	4
3648.2.cd	\(\chi_{3648}(239, \cdot)\)	n/a	624	4
3648.2.cg	\(\chi_{3648}(379, \cdot)\)	n/a	2560	8
3648.2.ch	\(\chi_{3648}(229, \cdot)\)	n/a	2304	8
3648.2.cj	\(\chi_{3648}(419, \cdot)\)	n/a	4608	8
3648.2.cm	\(\chi_{3648}(341, \cdot)\)	n/a	5088	8
3648.2.cp	\(\chi_{3648}(545, \cdot)\)	n/a	960	6
3648.2.cq	\(\chi_{3648}(289, \cdot)\)	n/a	480	6
3648.2.cs	\(\chi_{3648}(257, \cdot)\)	n/a	936	6
3648.2.cv	\(\chi_{3648}(223, \cdot)\)	n/a	480	6
3648.2.cx	\(\chi_{3648}(575, \cdot)\)	n/a	936	6
3648.2.cy	\(\chi_{3648}(127, \cdot)\)	n/a	480	6
3648.2.da	\(\chi_{3648}(479, \cdot)\)	n/a	960	6
3648.2.dc	\(\chi_{3648}(521, \cdot)\)	None	0	8
3648.2.dd	\(\chi_{3648}(311, \cdot)\)	None	0	8
3648.2.di	\(\chi_{3648}(103, \cdot)\)	None	0	8
3648.2.dj	\(\chi_{3648}(121, \cdot)\)	None	0	8
3648.2.dl	\(\chi_{3648}(79, \cdot)\)	n/a	960	12
3648.2.dn	\(\chi_{3648}(47, \cdot)\)	n/a	1872	12
3648.2.do	\(\chi_{3648}(529, \cdot)\)	n/a	960	12
3648.2.dq	\(\chi_{3648}(401, \cdot)\)	n/a	1872	12
3648.2.ds	\(\chi_{3648}(259, \cdot)\)	n/a	5120	16
3648.2.dv	\(\chi_{3648}(277, \cdot)\)	n/a	5120	16
3648.2.dx	\(\chi_{3648}(11, \cdot)\)	n/a	10176	16
3648.2.dy	\(\chi_{3648}(221, \cdot)\)	n/a	10176	16
3648.2.eb	\(\chi_{3648}(25, \cdot)\)	None	0	24
3648.2.ec	\(\chi_{3648}(295, \cdot)\)	None	0	24
3648.2.ee	\(\chi_{3648}(41, \cdot)\)	None	0	24
3648.2.eh	\(\chi_{3648}(23, \cdot)\)	None	0	24
3648.2.ei	\(\chi_{3648}(29, \cdot)\)	n/a	30528	48
3648.2.ek	\(\chi_{3648}(35, \cdot)\)	n/a	30528	48
3648.2.en	\(\chi_{3648}(61, \cdot)\)	n/a	15360	48
3648.2.ep	\(\chi_{3648}(67, \cdot)\)	n/a	15360	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3648))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3648)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(912))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1824))\)\(^{\oplus 2}\)