Space of modular forms of level 1160 and weight 2

• Label: 1160.2
• Level: 1160
• Weight: 2
• Dimension: 20416
• Nonzero newspaces: 32
• Sturm bound: 161280
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1160 = 2^{3} \cdot 5 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(161280\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1160))\).

	Total	New	Old
Modular forms	41664	21064	20600
Cusp forms	38977	20416	18561
Eisenstein series	2687	648	2039

Trace form

20416 * q - 48 * q^2 - 48 * q^3 - 48 * q^4 + 2 * q^5 - 152 * q^6 - 40 * q^7 - 48 * q^8 - 86 * q^9 - 76 * q^10 - 144 * q^11 - 72 * q^12 + 4 * q^13 - 72 * q^14 - 92 * q^15 - 184 * q^16 - 100 * q^17 - 104 * q^18 - 80 * q^19 - 116 * q^20 - 16 * q^21 - 88 * q^22 - 56 * q^23 - 104 * q^24 - 142 * q^25 - 184 * q^26 - 72 * q^27 - 40 * q^28 + 6 * q^29 - 168 * q^30 - 168 * q^31 - 8 * q^32 - 96 * q^33 + 16 * q^34 - 100 * q^35 - 88 * q^36 - 12 * q^37 - 8 * q^38 - 72 * q^39 + 4 * q^40 - 300 * q^41 - 8 * q^42 - 96 * q^43 - 24 * q^44 + 37 * q^45 - 104 * q^46 - 48 * q^47 - 40 * q^48 - 14 * q^49 - 116 * q^50 - 72 * q^51 - 96 * q^52 + 114 * q^53 - 104 * q^54 - 28 * q^55 - 264 * q^56 - 32 * q^57 - 100 * q^58 - 96 * q^59 - 164 * q^60 + 156 * q^61 - 168 * q^62 + 184 * q^63 - 120 * q^64 - 133 * q^65 - 200 * q^66 + 96 * q^67 - 96 * q^68 + 96 * q^69 - 84 * q^70 - 64 * q^71 - 32 * q^72 - 94 * q^73 - 16 * q^74 + 68 * q^75 - 168 * q^76 + 32 * q^77 + 72 * q^78 + 104 * q^79 - 36 * q^80 - 342 * q^81 + 16 * q^82 + 64 * q^83 - 160 * q^84 - 4 * q^85 - 184 * q^86 - 8 * q^87 - 112 * q^88 - 140 * q^89 - 76 * q^90 - 136 * q^91 - 24 * q^92 - 120 * q^94 - 60 * q^95 - 432 * q^96 - 126 * q^97 - 360 * q^98 - 384 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1160))\)

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
1160.2.a	\(\chi_{1160}(1, \cdot)\)	1160.2.a.a	1	1
		1160.2.a.b	1
		1160.2.a.c	1
		1160.2.a.d	1
		1160.2.a.e	3
		1160.2.a.f	3
		1160.2.a.g	3
		1160.2.a.h	5
		1160.2.a.i	5
		1160.2.a.j	5
1160.2.d	\(\chi_{1160}(929, \cdot)\)	1160.2.d.a	2	1
		1160.2.d.b	2
		1160.2.d.c	16
		1160.2.d.d	22
1160.2.e	\(\chi_{1160}(869, \cdot)\)	n/a	176	1
1160.2.f	\(\chi_{1160}(581, \cdot)\)	n/a	112	1
1160.2.g	\(\chi_{1160}(521, \cdot)\)	1160.2.g.a	2	1
		1160.2.g.b	14
		1160.2.g.c	14
1160.2.j	\(\chi_{1160}(289, \cdot)\)	1160.2.j.a	22	1
		1160.2.j.b	22
1160.2.k	\(\chi_{1160}(349, \cdot)\)	n/a	168	1
1160.2.p	\(\chi_{1160}(1101, \cdot)\)	n/a	120	1
1160.2.q	\(\chi_{1160}(133, \cdot)\)	n/a	352	2
1160.2.s	\(\chi_{1160}(17, \cdot)\)	1160.2.s.a	2	2
		1160.2.s.b	4
		1160.2.s.c	42
		1160.2.s.d	42
1160.2.u	\(\chi_{1160}(191, \cdot)\)	None	0	2
1160.2.w	\(\chi_{1160}(331, \cdot)\)	n/a	240	2
1160.2.ba	\(\chi_{1160}(407, \cdot)\)	None	0	2
1160.2.bb	\(\chi_{1160}(347, \cdot)\)	n/a	352	2
1160.2.bc	\(\chi_{1160}(523, \cdot)\)	n/a	336	2
1160.2.bd	\(\chi_{1160}(463, \cdot)\)	None	0	2
1160.2.bh	\(\chi_{1160}(99, \cdot)\)	n/a	352	2
1160.2.bj	\(\chi_{1160}(679, \cdot)\)	None	0	2
1160.2.bl	\(\chi_{1160}(713, \cdot)\)	1160.2.bl.a	2	2
		1160.2.bl.b	4
		1160.2.bl.c	42
		1160.2.bl.d	42
1160.2.bn	\(\chi_{1160}(597, \cdot)\)	n/a	352	2
1160.2.bo	\(\chi_{1160}(81, \cdot)\)	n/a	180	6
1160.2.bp	\(\chi_{1160}(341, \cdot)\)	n/a	720	6
1160.2.bu	\(\chi_{1160}(429, \cdot)\)	n/a	1056	6
1160.2.bv	\(\chi_{1160}(9, \cdot)\)	n/a	264	6
1160.2.by	\(\chi_{1160}(121, \cdot)\)	n/a	180	6
1160.2.bz	\(\chi_{1160}(141, \cdot)\)	n/a	720	6
1160.2.ca	\(\chi_{1160}(109, \cdot)\)	n/a	1056	6
1160.2.cb	\(\chi_{1160}(49, \cdot)\)	n/a	276	6
1160.2.ce	\(\chi_{1160}(97, \cdot)\)	n/a	540	12
1160.2.cg	\(\chi_{1160}(77, \cdot)\)	n/a	2112	12
1160.2.ci	\(\chi_{1160}(39, \cdot)\)	None	0	12
1160.2.ck	\(\chi_{1160}(19, \cdot)\)	n/a	2112	12
1160.2.co	\(\chi_{1160}(63, \cdot)\)	None	0	12
1160.2.cp	\(\chi_{1160}(83, \cdot)\)	n/a	2112	12
1160.2.cq	\(\chi_{1160}(67, \cdot)\)	n/a	2112	12
1160.2.cr	\(\chi_{1160}(7, \cdot)\)	None	0	12
1160.2.cv	\(\chi_{1160}(11, \cdot)\)	n/a	1440	12
1160.2.cx	\(\chi_{1160}(31, \cdot)\)	None	0	12
1160.2.cz	\(\chi_{1160}(37, \cdot)\)	n/a	2112	12
1160.2.db	\(\chi_{1160}(73, \cdot)\)	n/a	540	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1160))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1160)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(580))\)\(^{\oplus 2}\)