Space of modular forms of level 3528 and weight 2

• Label: 3528.2
• Level: 3528
• Weight: 2
• Dimension: 143857
• Nonzero newspaces: 60
• Sturm bound: 1354752
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(1354752\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3528))\).

	Total	New	Old
Modular forms	344448	145603	198845
Cusp forms	332929	143857	189072
Eisenstein series	11519	1746	9773

Trace form

143857 * q - 92 * q^2 - 123 * q^3 - 92 * q^4 + 4 * q^5 - 128 * q^6 - 108 * q^7 - 176 * q^8 - 249 * q^9 - 294 * q^10 - 95 * q^11 - 134 * q^12 + 10 * q^13 - 108 * q^14 - 240 * q^15 - 100 * q^16 - 188 * q^17 - 120 * q^18 - 292 * q^19 - 116 * q^20 - 208 * q^22 - 144 * q^23 - 96 * q^24 - 224 * q^25 - 122 * q^26 - 120 * q^27 - 372 * q^28 + 6 * q^29 - 74 * q^30 - 190 * q^31 - 112 * q^32 - 295 * q^33 - 176 * q^34 - 180 * q^35 - 166 * q^36 - 78 * q^37 - 88 * q^38 - 156 * q^39 - 140 * q^40 - 329 * q^41 - 144 * q^42 - 233 * q^43 - 94 * q^45 - 194 * q^46 - 228 * q^47 - 100 * q^48 - 270 * q^49 - 176 * q^50 - 183 * q^51 - 8 * q^52 - 122 * q^53 - 84 * q^54 - 394 * q^55 - 66 * q^56 - 461 * q^57 - 40 * q^58 - 161 * q^59 - 114 * q^60 - 8 * q^61 - 46 * q^62 - 144 * q^63 - 422 * q^64 - 214 * q^65 - 80 * q^66 - 103 * q^67 + 66 * q^68 + 94 * q^69 + 60 * q^70 + 62 * q^71 + 42 * q^72 - 480 * q^73 + 304 * q^74 + 145 * q^75 + 308 * q^76 + 126 * q^77 + 46 * q^78 + 206 * q^79 + 498 * q^80 - 157 * q^81 + 182 * q^82 + 266 * q^83 + 72 * q^84 + 212 * q^85 + 508 * q^86 + 114 * q^87 + 356 * q^88 - 110 * q^89 + 322 * q^90 - 228 * q^91 + 408 * q^92 + 134 * q^93 + 438 * q^94 + 250 * q^95 + 264 * q^96 - 261 * q^97 + 132 * q^98 - 210 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3528))\)

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
3528.2.a	\(\chi_{3528}(1, \cdot)\)	3528.2.a.a	1	1
		3528.2.a.b	1
		3528.2.a.c	1
		3528.2.a.d	1
		3528.2.a.e	1
		3528.2.a.f	1
		3528.2.a.g	1
		3528.2.a.h	1
		3528.2.a.i	1
		3528.2.a.j	1
		3528.2.a.k	1
		3528.2.a.l	1
		3528.2.a.m	1
		3528.2.a.n	1
		3528.2.a.o	1
		3528.2.a.p	1
		3528.2.a.q	1
		3528.2.a.r	1
		3528.2.a.s	1
		3528.2.a.t	1
		3528.2.a.u	1
		3528.2.a.v	1
		3528.2.a.w	1
		3528.2.a.x	1
		3528.2.a.y	1
		3528.2.a.z	1
		3528.2.a.ba	1
		3528.2.a.bb	2
		3528.2.a.bc	2
		3528.2.a.bd	2
		3528.2.a.be	2
		3528.2.a.bf	2
		3528.2.a.bg	2
		3528.2.a.bh	2
		3528.2.a.bi	2
		3528.2.a.bj	2
		3528.2.a.bk	2
		3528.2.a.bl	2
		3528.2.a.bm	2
3528.2.b	\(\chi_{3528}(1567, \cdot)\)	None	0	1
3528.2.c	\(\chi_{3528}(1765, \cdot)\)	n/a	200	1
3528.2.h	\(\chi_{3528}(1079, \cdot)\)	None	0	1
3528.2.i	\(\chi_{3528}(2645, \cdot)\)	n/a	160	1
3528.2.j	\(\chi_{3528}(2843, \cdot)\)	n/a	164	1
3528.2.k	\(\chi_{3528}(881, \cdot)\)	3528.2.k.a	8	1
		3528.2.k.b	16
		3528.2.k.c	16
3528.2.p	\(\chi_{3528}(3331, \cdot)\)	n/a	196	1
3528.2.q	\(\chi_{3528}(1537, \cdot)\)	n/a	240	2
3528.2.r	\(\chi_{3528}(1177, \cdot)\)	n/a	246	2
3528.2.s	\(\chi_{3528}(361, \cdot)\)	3528.2.s.a	2	2
		3528.2.s.b	2
		3528.2.s.c	2
		3528.2.s.d	2
		3528.2.s.e	2
		3528.2.s.f	2
		3528.2.s.g	2
		3528.2.s.h	2
		3528.2.s.i	2
		3528.2.s.j	2
		3528.2.s.k	2
		3528.2.s.l	2
		3528.2.s.m	2
		3528.2.s.n	2
		3528.2.s.o	2
		3528.2.s.p	2
		3528.2.s.q	2
		3528.2.s.r	2
		3528.2.s.s	2
		3528.2.s.t	2
		3528.2.s.u	2
		3528.2.s.v	2
		3528.2.s.w	2
		3528.2.s.x	2
		3528.2.s.y	2
		3528.2.s.z	2
		3528.2.s.ba	2
		3528.2.s.bb	2
		3528.2.s.bc	4
		3528.2.s.bd	4
		3528.2.s.be	4
		3528.2.s.bf	4
		3528.2.s.bg	4
		3528.2.s.bh	4
		3528.2.s.bi	4
		3528.2.s.bj	4
		3528.2.s.bk	4
		3528.2.s.bl	4
		3528.2.s.bm	4
3528.2.t	\(\chi_{3528}(961, \cdot)\)	n/a	240	2
3528.2.w	\(\chi_{3528}(949, \cdot)\)	n/a	944	2
3528.2.x	\(\chi_{3528}(31, \cdot)\)	None	0	2
3528.2.y	\(\chi_{3528}(1685, \cdot)\)	n/a	944	2
3528.2.z	\(\chi_{3528}(2615, \cdot)\)	None	0	2
3528.2.be	\(\chi_{3528}(979, \cdot)\)	n/a	944	2
3528.2.bf	\(\chi_{3528}(619, \cdot)\)	n/a	944	2
3528.2.bk	\(\chi_{3528}(19, \cdot)\)	n/a	392	2
3528.2.bl	\(\chi_{3528}(521, \cdot)\)	3528.2.bl.a	16	2
		3528.2.bl.b	16
		3528.2.bl.c	16
		3528.2.bl.d	32
3528.2.bm	\(\chi_{3528}(2627, \cdot)\)	n/a	320	2
3528.2.br	\(\chi_{3528}(491, \cdot)\)	n/a	964	2
3528.2.bs	\(\chi_{3528}(2273, \cdot)\)	n/a	240	2
3528.2.bt	\(\chi_{3528}(275, \cdot)\)	n/a	944	2
3528.2.bu	\(\chi_{3528}(2057, \cdot)\)	n/a	240	2
3528.2.bz	\(\chi_{3528}(2255, \cdot)\)	None	0	2
3528.2.ca	\(\chi_{3528}(509, \cdot)\)	n/a	944	2
3528.2.cb	\(\chi_{3528}(263, \cdot)\)	None	0	2
3528.2.cc	\(\chi_{3528}(293, \cdot)\)	n/a	944	2
3528.2.ch	\(\chi_{3528}(2285, \cdot)\)	n/a	320	2
3528.2.ci	\(\chi_{3528}(863, \cdot)\)	None	0	2
3528.2.cj	\(\chi_{3528}(1549, \cdot)\)	n/a	392	2
3528.2.ck	\(\chi_{3528}(1207, \cdot)\)	None	0	2
3528.2.cp	\(\chi_{3528}(391, \cdot)\)	None	0	2
3528.2.cq	\(\chi_{3528}(373, \cdot)\)	n/a	944	2
3528.2.cr	\(\chi_{3528}(607, \cdot)\)	None	0	2
3528.2.cs	\(\chi_{3528}(589, \cdot)\)	n/a	964	2
3528.2.cx	\(\chi_{3528}(1697, \cdot)\)	n/a	240	2
3528.2.cy	\(\chi_{3528}(851, \cdot)\)	n/a	944	2
3528.2.cz	\(\chi_{3528}(1195, \cdot)\)	n/a	944	2
3528.2.dc	\(\chi_{3528}(505, \cdot)\)	n/a	420	6
3528.2.dd	\(\chi_{3528}(307, \cdot)\)	n/a	1668	6
3528.2.di	\(\chi_{3528}(377, \cdot)\)	n/a	336	6
3528.2.dj	\(\chi_{3528}(323, \cdot)\)	n/a	1344	6
3528.2.dk	\(\chi_{3528}(125, \cdot)\)	n/a	1344	6
3528.2.dl	\(\chi_{3528}(71, \cdot)\)	None	0	6
3528.2.dq	\(\chi_{3528}(253, \cdot)\)	n/a	1668	6
3528.2.dr	\(\chi_{3528}(55, \cdot)\)	None	0	6
3528.2.ds	\(\chi_{3528}(193, \cdot)\)	n/a	2016	12
3528.2.dt	\(\chi_{3528}(289, \cdot)\)	n/a	840	12
3528.2.du	\(\chi_{3528}(169, \cdot)\)	n/a	2016	12
3528.2.dv	\(\chi_{3528}(25, \cdot)\)	n/a	2016	12
3528.2.dy	\(\chi_{3528}(187, \cdot)\)	n/a	8016	12
3528.2.dz	\(\chi_{3528}(347, \cdot)\)	n/a	8016	12
3528.2.ea	\(\chi_{3528}(185, \cdot)\)	n/a	2016	12
3528.2.ef	\(\chi_{3528}(85, \cdot)\)	n/a	8016	12
3528.2.eg	\(\chi_{3528}(103, \cdot)\)	None	0	12
3528.2.eh	\(\chi_{3528}(277, \cdot)\)	n/a	8016	12
3528.2.ei	\(\chi_{3528}(223, \cdot)\)	None	0	12
3528.2.en	\(\chi_{3528}(199, \cdot)\)	None	0	12
3528.2.eo	\(\chi_{3528}(37, \cdot)\)	n/a	3336	12
3528.2.ep	\(\chi_{3528}(359, \cdot)\)	None	0	12
3528.2.eq	\(\chi_{3528}(269, \cdot)\)	n/a	2688	12
3528.2.ev	\(\chi_{3528}(461, \cdot)\)	n/a	8016	12
3528.2.ew	\(\chi_{3528}(23, \cdot)\)	None	0	12
3528.2.ex	\(\chi_{3528}(5, \cdot)\)	n/a	8016	12
3528.2.ey	\(\chi_{3528}(239, \cdot)\)	None	0	12
3528.2.fd	\(\chi_{3528}(41, \cdot)\)	n/a	2016	12
3528.2.fe	\(\chi_{3528}(11, \cdot)\)	n/a	8016	12
3528.2.ff	\(\chi_{3528}(257, \cdot)\)	n/a	2016	12
3528.2.fg	\(\chi_{3528}(155, \cdot)\)	n/a	8016	12
3528.2.fl	\(\chi_{3528}(107, \cdot)\)	n/a	2688	12
3528.2.fm	\(\chi_{3528}(17, \cdot)\)	n/a	672	12
3528.2.fn	\(\chi_{3528}(451, \cdot)\)	n/a	3336	12
3528.2.fs	\(\chi_{3528}(115, \cdot)\)	n/a	8016	12
3528.2.ft	\(\chi_{3528}(139, \cdot)\)	n/a	8016	12
3528.2.fy	\(\chi_{3528}(95, \cdot)\)	None	0	12
3528.2.fz	\(\chi_{3528}(173, \cdot)\)	n/a	8016	12
3528.2.ga	\(\chi_{3528}(439, \cdot)\)	None	0	12
3528.2.gb	\(\chi_{3528}(205, \cdot)\)	n/a	8016	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3528))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3528)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1764))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3528))\)\(^{\oplus 1}\)