Space of modular forms of level 1360 and weight 2

• Label: 1360.2
• Level: 1360
• Weight: 2
• Dimension: 27908
• Nonzero newspaces: 50
• Sturm bound: 221184
• Trace bound: 15

Defining parameters

Level:	\( N \)	=	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 50 \)
Sturm bound:			\(221184\)
Trace bound:			\(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1360))\).

	Total	New	Old
Modular forms	57088	28720	28368
Cusp forms	53505	27908	25597
Eisenstein series	3583	812	2771

Trace form

27908 * q - 56 * q^2 - 44 * q^3 - 48 * q^4 - 104 * q^5 - 144 * q^6 - 36 * q^7 - 32 * q^8 - 8 * q^9 - 80 * q^10 - 112 * q^11 - 64 * q^12 - 60 * q^13 - 64 * q^14 - 28 * q^15 - 192 * q^16 - 126 * q^17 - 104 * q^18 + 8 * q^19 - 72 * q^20 - 152 * q^21 - 48 * q^22 - 12 * q^23 - 48 * q^24 - 4 * q^25 - 144 * q^26 - 56 * q^27 - 80 * q^28 - 40 * q^29 - 152 * q^30 - 200 * q^31 - 96 * q^32 - 160 * q^33 - 112 * q^34 - 164 * q^35 - 304 * q^36 - 116 * q^37 - 208 * q^38 - 88 * q^39 - 256 * q^40 - 104 * q^41 - 208 * q^42 - 28 * q^43 - 176 * q^44 - 156 * q^45 - 240 * q^46 + 28 * q^47 - 144 * q^48 - 112 * q^49 - 192 * q^50 - 108 * q^51 - 192 * q^52 - 36 * q^53 - 144 * q^54 + 16 * q^55 - 192 * q^56 + 192 * q^57 - 96 * q^58 + 104 * q^59 - 16 * q^60 - 112 * q^61 + 16 * q^62 + 188 * q^63 - 52 * q^65 - 16 * q^66 - 68 * q^67 + 72 * q^69 + 80 * q^70 - 136 * q^71 + 208 * q^72 + 156 * q^73 + 128 * q^74 - 140 * q^75 + 16 * q^76 + 64 * q^77 + 208 * q^78 - 128 * q^79 + 96 * q^80 - 188 * q^81 + 80 * q^82 - 124 * q^83 + 224 * q^84 - 94 * q^85 - 224 * q^86 - 280 * q^87 + 160 * q^88 + 32 * q^89 + 152 * q^90 - 168 * q^91 - 64 * q^92 + 32 * q^93 - 176 * q^95 - 96 * q^96 - 68 * q^97 - 136 * q^98 - 240 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1360))\)

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
1360.2.a	\(\chi_{1360}(1, \cdot)\)	1360.2.a.a	1	1
		1360.2.a.b	1
		1360.2.a.c	1
		1360.2.a.d	1
		1360.2.a.e	1
		1360.2.a.f	1
		1360.2.a.g	1
		1360.2.a.h	1
		1360.2.a.i	1
		1360.2.a.j	1
		1360.2.a.k	2
		1360.2.a.l	2
		1360.2.a.m	2
		1360.2.a.n	2
		1360.2.a.o	2
		1360.2.a.p	3
		1360.2.a.q	3
		1360.2.a.r	3
		1360.2.a.s	3
1360.2.c	\(\chi_{1360}(1121, \cdot)\)	1360.2.c.a	2	1
		1360.2.c.b	2
		1360.2.c.c	2
		1360.2.c.d	2
		1360.2.c.e	6
		1360.2.c.f	6
		1360.2.c.g	8
		1360.2.c.h	8
1360.2.e	\(\chi_{1360}(1089, \cdot)\)	1360.2.e.a	2	1
		1360.2.e.b	2
		1360.2.e.c	6
		1360.2.e.d	8
		1360.2.e.e	8
		1360.2.e.f	10
		1360.2.e.g	12
1360.2.f	\(\chi_{1360}(681, \cdot)\)	None	0	1
1360.2.h	\(\chi_{1360}(169, \cdot)\)	None	0	1
1360.2.j	\(\chi_{1360}(409, \cdot)\)	None	0	1
1360.2.l	\(\chi_{1360}(441, \cdot)\)	None	0	1
1360.2.o	\(\chi_{1360}(849, \cdot)\)	1360.2.o.a	2	1
		1360.2.o.b	2
		1360.2.o.c	4
		1360.2.o.d	4
		1360.2.o.e	8
		1360.2.o.f	8
		1360.2.o.g	24
1360.2.q	\(\chi_{1360}(47, \cdot)\)	n/a	108	2
1360.2.s	\(\chi_{1360}(21, \cdot)\)	n/a	288	2
1360.2.v	\(\chi_{1360}(747, \cdot)\)	n/a	424	2
1360.2.x	\(\chi_{1360}(307, \cdot)\)	n/a	384	2
1360.2.z	\(\chi_{1360}(149, \cdot)\)	n/a	424	2
1360.2.bb	\(\chi_{1360}(183, \cdot)\)	None	0	2
1360.2.bc	\(\chi_{1360}(523, \cdot)\)	n/a	424	2
1360.2.bf	\(\chi_{1360}(509, \cdot)\)	n/a	424	2
1360.2.bg	\(\chi_{1360}(341, \cdot)\)	n/a	256	2
1360.2.bj	\(\chi_{1360}(667, \cdot)\)	n/a	424	2
1360.2.bk	\(\chi_{1360}(407, \cdot)\)	None	0	2
1360.2.bn	\(\chi_{1360}(783, \cdot)\)	1360.2.bn.a	32	2
		1360.2.bn.b	64
1360.2.bp	\(\chi_{1360}(769, \cdot)\)	n/a	104	2
1360.2.bq	\(\chi_{1360}(361, \cdot)\)	None	0	2
1360.2.bt	\(\chi_{1360}(81, \cdot)\)	1360.2.bt.a	4	2
		1360.2.bt.b	8
		1360.2.bt.c	12
		1360.2.bt.d	12
		1360.2.bt.e	16
		1360.2.bt.f	20
1360.2.bu	\(\chi_{1360}(89, \cdot)\)	None	0	2
1360.2.bw	\(\chi_{1360}(103, \cdot)\)	None	0	2
1360.2.bz	\(\chi_{1360}(543, \cdot)\)	n/a	108	2
1360.2.ca	\(\chi_{1360}(803, \cdot)\)	n/a	424	2
1360.2.cd	\(\chi_{1360}(101, \cdot)\)	n/a	288	2
1360.2.ce	\(\chi_{1360}(69, \cdot)\)	n/a	384	2
1360.2.ch	\(\chi_{1360}(123, \cdot)\)	n/a	424	2
1360.2.cj	\(\chi_{1360}(727, \cdot)\)	None	0	2
1360.2.ck	\(\chi_{1360}(829, \cdot)\)	n/a	424	2
1360.2.cm	\(\chi_{1360}(987, \cdot)\)	n/a	384	2
1360.2.co	\(\chi_{1360}(67, \cdot)\)	n/a	424	2
1360.2.cr	\(\chi_{1360}(421, \cdot)\)	n/a	288	2
1360.2.cs	\(\chi_{1360}(863, \cdot)\)	n/a	108	2
1360.2.cv	\(\chi_{1360}(43, \cdot)\)	n/a	848	4
1360.2.cw	\(\chi_{1360}(161, \cdot)\)	n/a	144	4
1360.2.cz	\(\chi_{1360}(9, \cdot)\)	None	0	4
1360.2.db	\(\chi_{1360}(467, \cdot)\)	n/a	848	4
1360.2.dd	\(\chi_{1360}(189, \cdot)\)	n/a	848	4
1360.2.de	\(\chi_{1360}(461, \cdot)\)	n/a	576	4
1360.2.dg	\(\chi_{1360}(127, \cdot)\)	n/a	216	4
1360.2.dj	\(\chi_{1360}(287, \cdot)\)	n/a	216	4
1360.2.dk	\(\chi_{1360}(87, \cdot)\)	None	0	4
1360.2.dn	\(\chi_{1360}(247, \cdot)\)	None	0	4
1360.2.dp	\(\chi_{1360}(349, \cdot)\)	n/a	848	4
1360.2.dq	\(\chi_{1360}(621, \cdot)\)	n/a	576	4
1360.2.ds	\(\chi_{1360}(83, \cdot)\)	n/a	848	4
1360.2.dv	\(\chi_{1360}(49, \cdot)\)	n/a	208	4
1360.2.dw	\(\chi_{1360}(121, \cdot)\)	None	0	4
1360.2.dy	\(\chi_{1360}(427, \cdot)\)	n/a	848	4
1360.2.eb	\(\chi_{1360}(11, \cdot)\)	n/a	1152	8
1360.2.ed	\(\chi_{1360}(313, \cdot)\)	None	0	8
1360.2.ee	\(\chi_{1360}(177, \cdot)\)	n/a	416	8
1360.2.eg	\(\chi_{1360}(139, \cdot)\)	n/a	1696	8
1360.2.ej	\(\chi_{1360}(453, \cdot)\)	n/a	1696	8
1360.2.ek	\(\chi_{1360}(173, \cdot)\)	n/a	1696	8
1360.2.em	\(\chi_{1360}(71, \cdot)\)	None	0	8
1360.2.ep	\(\chi_{1360}(31, \cdot)\)	n/a	288	8
1360.2.er	\(\chi_{1360}(79, \cdot)\)	n/a	432	8
1360.2.es	\(\chi_{1360}(39, \cdot)\)	None	0	8
1360.2.ev	\(\chi_{1360}(37, \cdot)\)	n/a	1696	8
1360.2.ew	\(\chi_{1360}(133, \cdot)\)	n/a	1696	8
1360.2.ey	\(\chi_{1360}(99, \cdot)\)	n/a	1696	8
1360.2.fa	\(\chi_{1360}(97, \cdot)\)	n/a	416	8
1360.2.fd	\(\chi_{1360}(57, \cdot)\)	None	0	8
1360.2.ff	\(\chi_{1360}(211, \cdot)\)	n/a	1152	8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1360))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1360)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(680))\)\(^{\oplus 2}\)