Space of modular forms of level 1320 and weight 2

• Label: 1320.2
• Level: 1320
• Weight: 2
• Dimension: 17308
• Nonzero newspaces: 36
• Sturm bound: 184320
• Trace bound: 22

Defining parameters

Level:	\( N \)	=	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(184320\)
Trace bound:			\(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1320))\).

	Total	New	Old
Modular forms	48000	17740	30260
Cusp forms	44161	17308	26853
Eisenstein series	3839	432	3407

Trace form

17308 * q - 8 * q^2 - 24 * q^3 - 40 * q^4 - 8 * q^5 - 36 * q^6 - 56 * q^7 + 16 * q^8 - 40 * q^9 - 36 * q^10 + 24 * q^12 - 16 * q^13 + 64 * q^14 - 4 * q^15 - 24 * q^16 - 40 * q^17 + 20 * q^18 - 20 * q^19 + 64 * q^20 - 8 * q^21 - 8 * q^22 + 8 * q^23 - 4 * q^24 - 144 * q^25 + 32 * q^26 + 72 * q^27 - 40 * q^28 + 8 * q^29 + 8 * q^30 - 16 * q^31 - 8 * q^32 + 30 * q^33 + 48 * q^34 + 156 * q^35 + 116 * q^36 + 80 * q^37 + 120 * q^38 + 140 * q^39 - 48 * q^40 + 120 * q^41 + 136 * q^42 + 168 * q^43 + 224 * q^44 + 6 * q^45 + 32 * q^46 + 88 * q^47 + 56 * q^48 + 88 * q^49 + 36 * q^50 - 50 * q^51 + 176 * q^52 - 32 * q^53 + 68 * q^54 + 16 * q^55 + 128 * q^56 + 70 * q^57 - 32 * q^58 - 48 * q^59 - 124 * q^60 - 96 * q^61 - 16 * q^62 - 68 * q^63 - 136 * q^64 + 32 * q^65 - 124 * q^66 - 128 * q^67 - 112 * q^68 + 80 * q^69 - 344 * q^70 + 48 * q^71 - 204 * q^72 + 200 * q^73 - 312 * q^74 - 24 * q^75 - 504 * q^76 + 120 * q^77 - 424 * q^78 + 232 * q^79 - 380 * q^80 + 16 * q^81 - 696 * q^82 + 240 * q^83 - 404 * q^84 + 248 * q^85 - 288 * q^86 + 80 * q^87 - 632 * q^88 + 200 * q^89 - 122 * q^90 + 528 * q^91 - 304 * q^92 + 244 * q^93 - 264 * q^94 + 272 * q^95 - 96 * q^96 + 268 * q^97 - 240 * q^98 + 72 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1320))\)

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
1320.2.a	\(\chi_{1320}(1, \cdot)\)	1320.2.a.a	1	1
		1320.2.a.b	1
		1320.2.a.c	1
		1320.2.a.d	1
		1320.2.a.e	1
		1320.2.a.f	1
		1320.2.a.g	1
		1320.2.a.h	1
		1320.2.a.i	1
		1320.2.a.j	1
		1320.2.a.k	1
		1320.2.a.l	1
		1320.2.a.m	1
		1320.2.a.n	1
		1320.2.a.o	2
		1320.2.a.p	2
		1320.2.a.q	2
1320.2.d	\(\chi_{1320}(529, \cdot)\)	1320.2.d.a	6	1
		1320.2.d.b	6
		1320.2.d.c	10
		1320.2.d.d	10
1320.2.e	\(\chi_{1320}(1211, \cdot)\)	n/a	160	1
1320.2.f	\(\chi_{1320}(1121, \cdot)\)	1320.2.f.a	24	1
		1320.2.f.b	24
1320.2.g	\(\chi_{1320}(1099, \cdot)\)	n/a	144	1
1320.2.j	\(\chi_{1320}(1189, \cdot)\)	n/a	120	1
1320.2.k	\(\chi_{1320}(551, \cdot)\)	None	0	1
1320.2.p	\(\chi_{1320}(461, \cdot)\)	n/a	192	1
1320.2.q	\(\chi_{1320}(439, \cdot)\)	None	0	1
1320.2.t	\(\chi_{1320}(1231, \cdot)\)	None	0	1
1320.2.u	\(\chi_{1320}(989, \cdot)\)	n/a	280	1
1320.2.v	\(\chi_{1320}(1079, \cdot)\)	None	0	1
1320.2.w	\(\chi_{1320}(661, \cdot)\)	1320.2.w.a	2	1
		1320.2.w.b	2
		1320.2.w.c	12
		1320.2.w.d	18
		1320.2.w.e	20
		1320.2.w.f	26
1320.2.z	\(\chi_{1320}(571, \cdot)\)	1320.2.z.a	4	1
		1320.2.z.b	4
		1320.2.z.c	40
		1320.2.z.d	48
1320.2.ba	\(\chi_{1320}(329, \cdot)\)	1320.2.ba.a	72	1
1320.2.bf	\(\chi_{1320}(419, \cdot)\)	n/a	240	1
1320.2.bh	\(\chi_{1320}(263, \cdot)\)	None	0	2
1320.2.bi	\(\chi_{1320}(373, \cdot)\)	n/a	288	2
1320.2.bl	\(\chi_{1320}(67, \cdot)\)	n/a	240	2
1320.2.bm	\(\chi_{1320}(353, \cdot)\)	n/a	120	2
1320.2.bp	\(\chi_{1320}(463, \cdot)\)	None	0	2
1320.2.bq	\(\chi_{1320}(1013, \cdot)\)	n/a	480	2
1320.2.bt	\(\chi_{1320}(923, \cdot)\)	n/a	560	2
1320.2.bu	\(\chi_{1320}(1033, \cdot)\)	1320.2.bu.a	36	2
		1320.2.bu.b	36
1320.2.bw	\(\chi_{1320}(361, \cdot)\)	1320.2.bw.a	4	4
		1320.2.bw.b	8
		1320.2.bw.c	8
		1320.2.bw.d	12
		1320.2.bw.e	12
		1320.2.bw.f	12
		1320.2.bw.g	12
		1320.2.bw.h	12
		1320.2.bw.i	16
1320.2.bx	\(\chi_{1320}(59, \cdot)\)	n/a	1120	4
1320.2.cc	\(\chi_{1320}(211, \cdot)\)	n/a	384	4
1320.2.cd	\(\chi_{1320}(569, \cdot)\)	n/a	288	4
1320.2.cg	\(\chi_{1320}(119, \cdot)\)	None	0	4
1320.2.ch	\(\chi_{1320}(181, \cdot)\)	n/a	384	4
1320.2.ci	\(\chi_{1320}(151, \cdot)\)	None	0	4
1320.2.cj	\(\chi_{1320}(29, \cdot)\)	n/a	1120	4
1320.2.cm	\(\chi_{1320}(101, \cdot)\)	n/a	768	4
1320.2.cn	\(\chi_{1320}(79, \cdot)\)	None	0	4
1320.2.cs	\(\chi_{1320}(229, \cdot)\)	n/a	576	4
1320.2.ct	\(\chi_{1320}(71, \cdot)\)	None	0	4
1320.2.cw	\(\chi_{1320}(41, \cdot)\)	n/a	192	4
1320.2.cx	\(\chi_{1320}(19, \cdot)\)	n/a	576	4
1320.2.cy	\(\chi_{1320}(49, \cdot)\)	n/a	144	4
1320.2.cz	\(\chi_{1320}(251, \cdot)\)	n/a	768	4
1320.2.dd	\(\chi_{1320}(73, \cdot)\)	n/a	288	8
1320.2.de	\(\chi_{1320}(83, \cdot)\)	n/a	2240	8
1320.2.dh	\(\chi_{1320}(53, \cdot)\)	n/a	2240	8
1320.2.di	\(\chi_{1320}(103, \cdot)\)	None	0	8
1320.2.dl	\(\chi_{1320}(113, \cdot)\)	n/a	576	8
1320.2.dm	\(\chi_{1320}(163, \cdot)\)	n/a	1152	8
1320.2.dp	\(\chi_{1320}(13, \cdot)\)	n/a	1152	8
1320.2.dq	\(\chi_{1320}(167, \cdot)\)	None	0	8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1320))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1320)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1320))\)\(^{\oplus 1}\)