Space of modular forms of level 3552 and weight 2

• Label: 3552.2
• Level: 3552
• Weight: 2
• Dimension: 146828
• Nonzero newspaces: 60
• Sturm bound: 1400832
• Trace bound: 43

Defining parameters

Level:	\( N \)	=	\( 3552 = 2^{5} \cdot 3 \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(1400832\)
Trace bound:			\(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3552))\).

	Total	New	Old
Modular forms	354816	148228	206588
Cusp forms	345601	146828	198773
Eisenstein series	9215	1400	7815

Trace form

146828 * q - 104 * q^3 - 272 * q^4 - 8 * q^5 - 136 * q^6 - 208 * q^7 - 212 * q^9 - 240 * q^10 - 104 * q^12 - 248 * q^13 + 64 * q^14 - 84 * q^15 - 192 * q^16 + 32 * q^17 - 120 * q^18 - 192 * q^19 + 64 * q^20 - 104 * q^21 - 224 * q^22 + 48 * q^23 - 160 * q^24 - 372 * q^25 - 80 * q^26 - 32 * q^27 - 352 * q^28 - 8 * q^29 - 232 * q^30 - 112 * q^31 - 80 * q^32 - 344 * q^33 - 320 * q^34 + 96 * q^35 - 240 * q^36 - 300 * q^37 - 80 * q^38 - 68 * q^39 - 352 * q^40 - 16 * q^41 - 256 * q^42 - 208 * q^43 - 16 * q^44 - 208 * q^45 - 272 * q^46 - 48 * q^47 - 240 * q^48 - 220 * q^49 - 48 * q^50 - 140 * q^51 - 368 * q^52 + 24 * q^53 - 240 * q^54 - 328 * q^55 - 112 * q^56 - 248 * q^57 - 416 * q^58 - 128 * q^59 - 256 * q^60 - 152 * q^61 - 96 * q^62 - 132 * q^63 - 416 * q^64 - 16 * q^65 - 184 * q^66 - 304 * q^67 + 16 * q^68 - 8 * q^69 - 320 * q^70 - 80 * q^71 - 16 * q^72 - 328 * q^73 + 32 * q^74 - 292 * q^75 - 272 * q^76 + 128 * q^77 - 8 * q^78 - 208 * q^79 + 112 * q^80 + 4 * q^81 - 112 * q^82 + 128 * q^84 - 144 * q^85 + 128 * q^86 - 236 * q^87 - 96 * q^88 + 128 * q^90 - 200 * q^91 + 160 * q^92 - 160 * q^93 - 96 * q^94 - 32 * q^95 + 144 * q^96 - 664 * q^97 + 160 * q^98 - 260 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3552))\)

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
3552.2.a	\(\chi_{3552}(1, \cdot)\)	3552.2.a.a	1	1
		3552.2.a.b	1
		3552.2.a.c	1
		3552.2.a.d	1
		3552.2.a.e	1
		3552.2.a.f	1
		3552.2.a.g	3
		3552.2.a.h	3
		3552.2.a.i	3
		3552.2.a.j	3
		3552.2.a.k	3
		3552.2.a.l	3
		3552.2.a.m	4
		3552.2.a.n	4
		3552.2.a.o	4
		3552.2.a.p	4
		3552.2.a.q	4
		3552.2.a.r	4
		3552.2.a.s	5
		3552.2.a.t	5
		3552.2.a.u	7
		3552.2.a.v	7
3552.2.c	\(\chi_{3552}(1775, \cdot)\)	n/a	148	1
3552.2.e	\(\chi_{3552}(2591, \cdot)\)	n/a	144	1
3552.2.f	\(\chi_{3552}(1777, \cdot)\)	3552.2.f.a	28	1
		3552.2.f.b	44
3552.2.h	\(\chi_{3552}(961, \cdot)\)	3552.2.h.a	6	1
		3552.2.h.b	6
		3552.2.h.c	12
		3552.2.h.d	12
		3552.2.h.e	20
		3552.2.h.f	20
3552.2.j	\(\chi_{3552}(815, \cdot)\)	n/a	144	1
3552.2.l	\(\chi_{3552}(3551, \cdot)\)	n/a	152	1
3552.2.o	\(\chi_{3552}(2737, \cdot)\)	3552.2.o.a	76	1
3552.2.q	\(\chi_{3552}(2209, \cdot)\)	n/a	152	2
3552.2.r	\(\chi_{3552}(2633, \cdot)\)	None	0	2
3552.2.u	\(\chi_{3552}(487, \cdot)\)	None	0	2
3552.2.v	\(\chi_{3552}(1807, \cdot)\)	n/a	152	2
3552.2.x	\(\chi_{3552}(73, \cdot)\)	None	0	2
3552.2.ba	\(\chi_{3552}(889, \cdot)\)	None	0	2
3552.2.bb	\(\chi_{3552}(31, \cdot)\)	n/a	152	2
3552.2.be	\(\chi_{3552}(401, \cdot)\)	n/a	296	2
3552.2.bf	\(\chi_{3552}(1703, \cdot)\)	None	0	2
3552.2.bi	\(\chi_{3552}(887, \cdot)\)	None	0	2
3552.2.bk	\(\chi_{3552}(2177, \cdot)\)	n/a	304	2
3552.2.bm	\(\chi_{3552}(857, \cdot)\)	None	0	2
3552.2.bn	\(\chi_{3552}(2263, \cdot)\)	None	0	2
3552.2.bp	\(\chi_{3552}(529, \cdot)\)	n/a	152	2
3552.2.bt	\(\chi_{3552}(47, \cdot)\)	n/a	296	2
3552.2.bv	\(\chi_{3552}(767, \cdot)\)	n/a	304	2
3552.2.bx	\(\chi_{3552}(433, \cdot)\)	n/a	152	2
3552.2.bz	\(\chi_{3552}(1729, \cdot)\)	n/a	152	2
3552.2.ca	\(\chi_{3552}(2543, \cdot)\)	n/a	296	2
3552.2.cc	\(\chi_{3552}(1247, \cdot)\)	n/a	304	2
3552.2.cg	\(\chi_{3552}(443, \cdot)\)	n/a	2416	4
3552.2.ch	\(\chi_{3552}(445, \cdot)\)	n/a	1152	4
3552.2.ck	\(\chi_{3552}(845, \cdot)\)	n/a	2416	4
3552.2.cl	\(\chi_{3552}(43, \cdot)\)	n/a	1216	4
3552.2.co	\(\chi_{3552}(475, \cdot)\)	n/a	1216	4
3552.2.cp	\(\chi_{3552}(413, \cdot)\)	n/a	2416	4
3552.2.cq	\(\chi_{3552}(371, \cdot)\)	n/a	2304	4
3552.2.cr	\(\chi_{3552}(517, \cdot)\)	n/a	1216	4
3552.2.cu	\(\chi_{3552}(673, \cdot)\)	n/a	456	6
3552.2.cw	\(\chi_{3552}(103, \cdot)\)	None	0	4
3552.2.cx	\(\chi_{3552}(2249, \cdot)\)	None	0	4
3552.2.cz	\(\chi_{3552}(689, \cdot)\)	n/a	592	4
3552.2.dc	\(\chi_{3552}(455, \cdot)\)	None	0	4
3552.2.dd	\(\chi_{3552}(359, \cdot)\)	None	0	4
3552.2.df	\(\chi_{3552}(2465, \cdot)\)	n/a	608	4
3552.2.di	\(\chi_{3552}(2095, \cdot)\)	n/a	304	4
3552.2.dk	\(\chi_{3552}(121, \cdot)\)	None	0	4
3552.2.dl	\(\chi_{3552}(841, \cdot)\)	None	0	4
3552.2.do	\(\chi_{3552}(319, \cdot)\)	n/a	304	4
3552.2.dp	\(\chi_{3552}(1879, \cdot)\)	None	0	4
3552.2.ds	\(\chi_{3552}(473, \cdot)\)	None	0	4
3552.2.du	\(\chi_{3552}(863, \cdot)\)	n/a	912	6
3552.2.dx	\(\chi_{3552}(95, \cdot)\)	n/a	912	6
3552.2.dy	\(\chi_{3552}(289, \cdot)\)	n/a	456	6
3552.2.eb	\(\chi_{3552}(527, \cdot)\)	n/a	888	6
3552.2.ec	\(\chi_{3552}(49, \cdot)\)	n/a	456	6
3552.2.ef	\(\chi_{3552}(337, \cdot)\)	n/a	456	6
3552.2.eg	\(\chi_{3552}(1103, \cdot)\)	n/a	888	6
3552.2.ei	\(\chi_{3552}(85, \cdot)\)	n/a	2432	8
3552.2.ej	\(\chi_{3552}(491, \cdot)\)	n/a	4832	8
3552.2.eo	\(\chi_{3552}(547, \cdot)\)	n/a	2432	8
3552.2.ep	\(\chi_{3552}(29, \cdot)\)	n/a	4832	8
3552.2.es	\(\chi_{3552}(917, \cdot)\)	n/a	4832	8
3552.2.et	\(\chi_{3552}(1435, \cdot)\)	n/a	2432	8
3552.2.ew	\(\chi_{3552}(565, \cdot)\)	n/a	2432	8
3552.2.ex	\(\chi_{3552}(11, \cdot)\)	n/a	4832	8
3552.2.fa	\(\chi_{3552}(161, \cdot)\)	n/a	1824	12
3552.2.fb	\(\chi_{3552}(607, \cdot)\)	n/a	912	12
3552.2.fc	\(\chi_{3552}(25, \cdot)\)	None	0	12
3552.2.fe	\(\chi_{3552}(215, \cdot)\)	None	0	12
3552.2.fg	\(\chi_{3552}(281, \cdot)\)	None	0	12
3552.2.fh	\(\chi_{3552}(535, \cdot)\)	None	0	12
3552.2.fm	\(\chi_{3552}(89, \cdot)\)	None	0	12
3552.2.fn	\(\chi_{3552}(55, \cdot)\)	None	0	12
3552.2.fo	\(\chi_{3552}(71, \cdot)\)	None	0	12
3552.2.fq	\(\chi_{3552}(601, \cdot)\)	None	0	12
3552.2.fu	\(\chi_{3552}(79, \cdot)\)	n/a	912	12
3552.2.fv	\(\chi_{3552}(17, \cdot)\)	n/a	1776	12
3552.2.fw	\(\chi_{3552}(19, \cdot)\)	n/a	7296	24
3552.2.fx	\(\chi_{3552}(461, \cdot)\)	n/a	14496	24
3552.2.gc	\(\chi_{3552}(83, \cdot)\)	n/a	14496	24
3552.2.gd	\(\chi_{3552}(373, \cdot)\)	n/a	7296	24
3552.2.gg	\(\chi_{3552}(157, \cdot)\)	n/a	7296	24
3552.2.gh	\(\chi_{3552}(299, \cdot)\)	n/a	14496	24
3552.2.gi	\(\chi_{3552}(5, \cdot)\)	n/a	14496	24
3552.2.gj	\(\chi_{3552}(91, \cdot)\)	n/a	7296	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3552))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3552)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1776))\)\(^{\oplus 2}\)