Space of modular forms of level 1140 and weight 2

• Label: 1140.2
• Level: 1140
• Weight: 2
• Dimension: 13576
• Nonzero newspaces: 36
• Sturm bound: 138240
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(138240\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1140))\).

	Total	New	Old
Modular forms	36000	13992	22008
Cusp forms	33121	13576	19545
Eisenstein series	2879	416	2463

Trace form

13576 * q - 4 * q^3 - 20 * q^4 - 4 * q^5 - 38 * q^6 + 8 * q^7 + 24 * q^8 - 16 * q^9 - 14 * q^10 + 16 * q^11 - 10 * q^12 - 72 * q^13 + 10 * q^15 - 108 * q^16 + 4 * q^17 - 32 * q^18 - 84 * q^19 - 40 * q^20 - 126 * q^21 - 52 * q^22 - 36 * q^23 - 66 * q^24 - 116 * q^25 - 32 * q^26 - 16 * q^27 + 24 * q^28 + 48 * q^29 - 36 * q^30 + 24 * q^31 + 140 * q^32 + 48 * q^33 + 96 * q^34 + 40 * q^35 + 126 * q^36 + 72 * q^37 + 236 * q^38 + 108 * q^39 + 40 * q^40 + 80 * q^41 + 146 * q^42 + 168 * q^43 + 180 * q^44 + 31 * q^45 + 120 * q^46 + 72 * q^47 + 148 * q^48 + 36 * q^49 + 86 * q^50 + 132 * q^51 + 44 * q^52 - 8 * q^53 + 94 * q^54 + 16 * q^55 + 128 * q^56 + 34 * q^57 + 40 * q^58 + 16 * q^59 + 110 * q^60 + 24 * q^61 - 68 * q^62 + 68 * q^63 - 212 * q^64 + 68 * q^65 - 70 * q^66 + 152 * q^67 - 220 * q^68 + 242 * q^69 - 254 * q^70 + 72 * q^71 - 150 * q^72 + 156 * q^73 - 288 * q^74 + 8 * q^75 - 500 * q^76 + 444 * q^77 - 194 * q^78 + 192 * q^79 - 152 * q^80 - 88 * q^81 - 688 * q^82 + 180 * q^83 - 346 * q^84 + 284 * q^85 - 380 * q^86 + 176 * q^87 - 532 * q^88 + 284 * q^89 - 210 * q^90 + 192 * q^91 - 292 * q^92 + 144 * q^93 - 352 * q^94 + 162 * q^95 - 380 * q^96 + 100 * q^97 - 48 * q^98 + 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1140))\)

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
1140.2.a	\(\chi_{1140}(1, \cdot)\)	1140.2.a.a	1	1
		1140.2.a.b	1
		1140.2.a.c	1
		1140.2.a.d	1
		1140.2.a.e	2
		1140.2.a.f	3
		1140.2.a.g	3
1140.2.b	\(\chi_{1140}(151, \cdot)\)	1140.2.b.a	2	1
		1140.2.b.b	2
		1140.2.b.c	18
		1140.2.b.d	18
		1140.2.b.e	20
		1140.2.b.f	20
1140.2.e	\(\chi_{1140}(569, \cdot)\)	1140.2.e.a	16	1
		1140.2.e.b	24
1140.2.f	\(\chi_{1140}(229, \cdot)\)	1140.2.f.a	6	1
		1140.2.f.b	10
1140.2.i	\(\chi_{1140}(191, \cdot)\)	n/a	144	1
1140.2.j	\(\chi_{1140}(341, \cdot)\)	1140.2.j.a	28	1
1140.2.m	\(\chi_{1140}(379, \cdot)\)	n/a	120	1
1140.2.n	\(\chi_{1140}(419, \cdot)\)	n/a	216	1
1140.2.q	\(\chi_{1140}(121, \cdot)\)	1140.2.q.a	2	2
		1140.2.q.b	2
		1140.2.q.c	2
		1140.2.q.d	2
		1140.2.q.e	2
		1140.2.q.f	2
		1140.2.q.g	2
		1140.2.q.h	2
		1140.2.q.i	2
		1140.2.q.j	2
		1140.2.q.k	2
		1140.2.q.l	2
1140.2.s	\(\chi_{1140}(343, \cdot)\)	n/a	216	2
1140.2.u	\(\chi_{1140}(77, \cdot)\)	1140.2.u.a	36	2
		1140.2.u.b	36
1140.2.w	\(\chi_{1140}(227, \cdot)\)	n/a	464	2
1140.2.y	\(\chi_{1140}(37, \cdot)\)	1140.2.y.a	40	2
1140.2.z	\(\chi_{1140}(449, \cdot)\)	1140.2.z.a	80	2
1140.2.bc	\(\chi_{1140}(31, \cdot)\)	n/a	160	2
1140.2.bd	\(\chi_{1140}(11, \cdot)\)	n/a	320	2
1140.2.bg	\(\chi_{1140}(49, \cdot)\)	1140.2.bg.a	4	2
		1140.2.bg.b	4
		1140.2.bg.c	32
1140.2.bh	\(\chi_{1140}(259, \cdot)\)	n/a	240	2
1140.2.bk	\(\chi_{1140}(221, \cdot)\)	1140.2.bk.a	56	2
1140.2.bn	\(\chi_{1140}(239, \cdot)\)	n/a	464	2
1140.2.bo	\(\chi_{1140}(61, \cdot)\)	1140.2.bo.a	18	6
		1140.2.bo.b	18
		1140.2.bo.c	24
		1140.2.bo.d	24
1140.2.bp	\(\chi_{1140}(197, \cdot)\)	n/a	160	4
1140.2.br	\(\chi_{1140}(7, \cdot)\)	n/a	480	4
1140.2.bt	\(\chi_{1140}(217, \cdot)\)	1140.2.bt.a	80	4
1140.2.bv	\(\chi_{1140}(107, \cdot)\)	n/a	928	4
1140.2.bz	\(\chi_{1140}(119, \cdot)\)	n/a	1392	6
1140.2.ca	\(\chi_{1140}(79, \cdot)\)	n/a	720	6
1140.2.cd	\(\chi_{1140}(41, \cdot)\)	n/a	156	6
1140.2.cf	\(\chi_{1140}(169, \cdot)\)	n/a	120	6
1140.2.cg	\(\chi_{1140}(131, \cdot)\)	n/a	960	6
1140.2.cj	\(\chi_{1140}(91, \cdot)\)	n/a	480	6
1140.2.ck	\(\chi_{1140}(29, \cdot)\)	n/a	240	6
1140.2.cm	\(\chi_{1140}(143, \cdot)\)	n/a	2784	12
1140.2.co	\(\chi_{1140}(13, \cdot)\)	n/a	240	12
1140.2.cq	\(\chi_{1140}(17, \cdot)\)	n/a	480	12
1140.2.cs	\(\chi_{1140}(43, \cdot)\)	n/a	1440	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1140))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1140)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 2}\)