Space of modular forms of level 3960 and weight 2

• Label: 3960.2
• Level: 3960
• Weight: 2
• Dimension: 165496
• Nonzero newspaces: 72
• Sturm bound: 1658880
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 72 \)
Sturm bound:			\(1658880\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3960))\).

	Total	New	Old
Modular forms	422400	167440	254960
Cusp forms	407041	165496	241545
Eisenstein series	15359	1944	13415

Trace form

165496 * q - 44 * q^2 - 60 * q^3 - 44 * q^4 + 10 * q^5 - 208 * q^6 - 36 * q^7 - 92 * q^8 - 132 * q^9 - 246 * q^10 - 186 * q^11 - 184 * q^12 - 4 * q^13 - 116 * q^14 - 136 * q^15 - 204 * q^16 - 136 * q^17 - 48 * q^18 - 198 * q^19 - 86 * q^20 - 64 * q^21 - 40 * q^22 - 220 * q^23 + 48 * q^24 - 162 * q^25 - 52 * q^26 - 96 * q^27 - 68 * q^28 - 40 * q^29 + 4 * q^30 - 256 * q^31 + 136 * q^32 - 166 * q^33 - 168 * q^34 - 144 * q^35 + 24 * q^36 - 52 * q^37 + 120 * q^38 + 64 * q^39 - 36 * q^40 - 372 * q^41 + 200 * q^42 - 64 * q^43 - 28 * q^44 + 4 * q^45 - 360 * q^46 + 112 * q^47 + 144 * q^48 - 274 * q^49 + 180 * q^50 - 64 * q^51 + 32 * q^52 - 92 * q^53 + 112 * q^54 - 276 * q^55 - 184 * q^56 - 276 * q^57 + 192 * q^58 + 30 * q^59 + 20 * q^60 - 108 * q^61 + 68 * q^62 + 64 * q^63 + 124 * q^64 - 172 * q^65 - 304 * q^66 - 212 * q^67 - 4 * q^68 - 24 * q^69 + 224 * q^70 - 156 * q^71 - 296 * q^72 - 480 * q^73 - 120 * q^74 + 104 * q^75 - 60 * q^76 - 228 * q^77 - 360 * q^78 - 300 * q^79 + 52 * q^80 - 260 * q^81 + 236 * q^82 + 54 * q^83 - 240 * q^84 - 160 * q^85 - 84 * q^86 + 232 * q^87 + 296 * q^88 - 112 * q^89 - 116 * q^90 - 608 * q^91 + 236 * q^92 + 152 * q^93 + 228 * q^94 + 158 * q^95 + 136 * q^96 - 118 * q^97 + 312 * q^98 + 148 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3960))\)

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
3960.2.a	\(\chi_{3960}(1, \cdot)\)	3960.2.a.a	1	1
		3960.2.a.b	1
		3960.2.a.c	1
		3960.2.a.d	1
		3960.2.a.e	1
		3960.2.a.f	1
		3960.2.a.g	1
		3960.2.a.h	1
		3960.2.a.i	1
		3960.2.a.j	1
		3960.2.a.k	1
		3960.2.a.l	1
		3960.2.a.m	1
		3960.2.a.n	1
		3960.2.a.o	1
		3960.2.a.p	1
		3960.2.a.q	1
		3960.2.a.r	1
		3960.2.a.s	1
		3960.2.a.t	1
		3960.2.a.u	2
		3960.2.a.v	2
		3960.2.a.w	2
		3960.2.a.x	2
		3960.2.a.y	2
		3960.2.a.z	2
		3960.2.a.ba	2
		3960.2.a.bb	2
		3960.2.a.bc	2
		3960.2.a.bd	2
		3960.2.a.be	2
		3960.2.a.bf	2
		3960.2.a.bg	3
		3960.2.a.bh	3
3960.2.d	\(\chi_{3960}(3169, \cdot)\)	3960.2.d.a	2	1
		3960.2.d.b	2
		3960.2.d.c	2
		3960.2.d.d	6
		3960.2.d.e	6
		3960.2.d.f	8
		3960.2.d.g	10
		3960.2.d.h	10
		3960.2.d.i	14
		3960.2.d.j	14
3960.2.e	\(\chi_{3960}(3851, \cdot)\)	n/a	160	1
3960.2.f	\(\chi_{3960}(3761, \cdot)\)	3960.2.f.a	12	1
		3960.2.f.b	12
		3960.2.f.c	12
		3960.2.f.d	12
3960.2.g	\(\chi_{3960}(1099, \cdot)\)	n/a	356	1
3960.2.j	\(\chi_{3960}(1189, \cdot)\)	n/a	300	1
3960.2.k	\(\chi_{3960}(1871, \cdot)\)	None	0	1
3960.2.p	\(\chi_{3960}(1781, \cdot)\)	n/a	192	1
3960.2.q	\(\chi_{3960}(3079, \cdot)\)	None	0	1
3960.2.t	\(\chi_{3960}(3871, \cdot)\)	None	0	1
3960.2.u	\(\chi_{3960}(989, \cdot)\)	n/a	288	1
3960.2.v	\(\chi_{3960}(1079, \cdot)\)	None	0	1
3960.2.w	\(\chi_{3960}(1981, \cdot)\)	n/a	200	1
3960.2.z	\(\chi_{3960}(1891, \cdot)\)	n/a	240	1
3960.2.ba	\(\chi_{3960}(2969, \cdot)\)	3960.2.ba.a	4	1
		3960.2.ba.b	4
		3960.2.ba.c	64
3960.2.bf	\(\chi_{3960}(3059, \cdot)\)	n/a	240	1
3960.2.bg	\(\chi_{3960}(1321, \cdot)\)	n/a	240	2
3960.2.bi	\(\chi_{3960}(1583, \cdot)\)	None	0	2
3960.2.bj	\(\chi_{3960}(1693, \cdot)\)	n/a	712	2
3960.2.bm	\(\chi_{3960}(1387, \cdot)\)	n/a	600	2
3960.2.bn	\(\chi_{3960}(1673, \cdot)\)	n/a	120	2
3960.2.bq	\(\chi_{3960}(1783, \cdot)\)	None	0	2
3960.2.br	\(\chi_{3960}(1277, \cdot)\)	n/a	480	2
3960.2.bu	\(\chi_{3960}(1187, \cdot)\)	n/a	576	2
3960.2.bv	\(\chi_{3960}(1297, \cdot)\)	n/a	180	2
3960.2.bx	\(\chi_{3960}(361, \cdot)\)	n/a	240	4
3960.2.by	\(\chi_{3960}(329, \cdot)\)	n/a	432	2
3960.2.bz	\(\chi_{3960}(571, \cdot)\)	n/a	1152	2
3960.2.ce	\(\chi_{3960}(419, \cdot)\)	n/a	1440	2
3960.2.ch	\(\chi_{3960}(2309, \cdot)\)	n/a	1712	2
3960.2.ci	\(\chi_{3960}(1231, \cdot)\)	None	0	2
3960.2.cj	\(\chi_{3960}(661, \cdot)\)	n/a	960	2
3960.2.ck	\(\chi_{3960}(2399, \cdot)\)	None	0	2
3960.2.cn	\(\chi_{3960}(551, \cdot)\)	None	0	2
3960.2.co	\(\chi_{3960}(2509, \cdot)\)	n/a	1440	2
3960.2.ct	\(\chi_{3960}(439, \cdot)\)	None	0	2
3960.2.cu	\(\chi_{3960}(461, \cdot)\)	n/a	1152	2
3960.2.cx	\(\chi_{3960}(1211, \cdot)\)	n/a	960	2
3960.2.cy	\(\chi_{3960}(529, \cdot)\)	n/a	360	2
3960.2.cz	\(\chi_{3960}(2419, \cdot)\)	n/a	1712	2
3960.2.da	\(\chi_{3960}(1121, \cdot)\)	n/a	288	2
3960.2.dd	\(\chi_{3960}(179, \cdot)\)	n/a	1152	4
3960.2.di	\(\chi_{3960}(811, \cdot)\)	n/a	960	4
3960.2.dj	\(\chi_{3960}(809, \cdot)\)	n/a	288	4
3960.2.dm	\(\chi_{3960}(719, \cdot)\)	None	0	4
3960.2.dn	\(\chi_{3960}(181, \cdot)\)	n/a	960	4
3960.2.do	\(\chi_{3960}(271, \cdot)\)	None	0	4
3960.2.dp	\(\chi_{3960}(629, \cdot)\)	n/a	1152	4
3960.2.ds	\(\chi_{3960}(701, \cdot)\)	n/a	768	4
3960.2.dt	\(\chi_{3960}(919, \cdot)\)	None	0	4
3960.2.dy	\(\chi_{3960}(829, \cdot)\)	n/a	1424	4
3960.2.dz	\(\chi_{3960}(71, \cdot)\)	None	0	4
3960.2.ec	\(\chi_{3960}(161, \cdot)\)	n/a	192	4
3960.2.ed	\(\chi_{3960}(19, \cdot)\)	n/a	1424	4
3960.2.ee	\(\chi_{3960}(289, \cdot)\)	n/a	360	4
3960.2.ef	\(\chi_{3960}(251, \cdot)\)	n/a	768	4
3960.2.ej	\(\chi_{3960}(353, \cdot)\)	n/a	720	4
3960.2.ek	\(\chi_{3960}(67, \cdot)\)	n/a	2880	4
3960.2.en	\(\chi_{3960}(373, \cdot)\)	n/a	3424	4
3960.2.eo	\(\chi_{3960}(263, \cdot)\)	None	0	4
3960.2.er	\(\chi_{3960}(1033, \cdot)\)	n/a	864	4
3960.2.es	\(\chi_{3960}(923, \cdot)\)	n/a	3424	4
3960.2.ev	\(\chi_{3960}(1013, \cdot)\)	n/a	2880	4
3960.2.ew	\(\chi_{3960}(463, \cdot)\)	None	0	4
3960.2.ey	\(\chi_{3960}(841, \cdot)\)	n/a	1152	8
3960.2.fa	\(\chi_{3960}(73, \cdot)\)	n/a	720	8
3960.2.fb	\(\chi_{3960}(107, \cdot)\)	n/a	2304	8
3960.2.fe	\(\chi_{3960}(53, \cdot)\)	n/a	2304	8
3960.2.ff	\(\chi_{3960}(487, \cdot)\)	None	0	8
3960.2.fi	\(\chi_{3960}(377, \cdot)\)	n/a	576	8
3960.2.fj	\(\chi_{3960}(163, \cdot)\)	n/a	2848	8
3960.2.fm	\(\chi_{3960}(613, \cdot)\)	n/a	2848	8
3960.2.fn	\(\chi_{3960}(503, \cdot)\)	None	0	8
3960.2.fr	\(\chi_{3960}(139, \cdot)\)	n/a	6848	8
3960.2.fs	\(\chi_{3960}(41, \cdot)\)	n/a	1152	8
3960.2.ft	\(\chi_{3960}(731, \cdot)\)	n/a	4608	8
3960.2.fu	\(\chi_{3960}(49, \cdot)\)	n/a	1728	8
3960.2.fx	\(\chi_{3960}(79, \cdot)\)	None	0	8
3960.2.fy	\(\chi_{3960}(101, \cdot)\)	n/a	4608	8
3960.2.gd	\(\chi_{3960}(191, \cdot)\)	None	0	8
3960.2.ge	\(\chi_{3960}(229, \cdot)\)	n/a	6848	8
3960.2.gh	\(\chi_{3960}(301, \cdot)\)	n/a	4608	8
3960.2.gi	\(\chi_{3960}(119, \cdot)\)	None	0	8
3960.2.gj	\(\chi_{3960}(29, \cdot)\)	n/a	6848	8
3960.2.gk	\(\chi_{3960}(151, \cdot)\)	None	0	8
3960.2.gn	\(\chi_{3960}(59, \cdot)\)	n/a	6848	8
3960.2.gs	\(\chi_{3960}(569, \cdot)\)	n/a	1728	8
3960.2.gt	\(\chi_{3960}(211, \cdot)\)	n/a	4608	8
3960.2.gv	\(\chi_{3960}(103, \cdot)\)	None	0	16
3960.2.gw	\(\chi_{3960}(317, \cdot)\)	n/a	13696	16
3960.2.gz	\(\chi_{3960}(83, \cdot)\)	n/a	13696	16
3960.2.ha	\(\chi_{3960}(193, \cdot)\)	n/a	3456	16
3960.2.hd	\(\chi_{3960}(167, \cdot)\)	None	0	16
3960.2.he	\(\chi_{3960}(13, \cdot)\)	n/a	13696	16
3960.2.hh	\(\chi_{3960}(427, \cdot)\)	n/a	13696	16
3960.2.hi	\(\chi_{3960}(113, \cdot)\)	n/a	3456	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3960)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(990))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1980))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3960))\)\(^{\oplus 1}\)