Space of modular forms of level 760 and weight 2

• Label: 760.2
• Level: 760
• Weight: 2
• Dimension: 8656
• Nonzero newspaces: 27
• Newform subspaces: 68
• Sturm bound: 69120
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 27 \)
Newform subspaces:			\( 68 \)
Sturm bound:			\(69120\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(760))\).

	Total	New	Old
Modular forms	18144	9064	9080
Cusp forms	16417	8656	7761
Eisenstein series	1727	408	1319

Trace form

8656 * q - 28 * q^2 - 28 * q^3 - 28 * q^4 + 2 * q^5 - 92 * q^6 - 20 * q^7 - 28 * q^8 - 46 * q^9 - 46 * q^10 - 84 * q^11 - 52 * q^12 + 4 * q^13 - 52 * q^14 - 62 * q^15 - 124 * q^16 - 60 * q^17 - 84 * q^18 - 48 * q^19 - 140 * q^20 - 16 * q^21 - 68 * q^22 - 36 * q^23 - 84 * q^24 - 82 * q^25 - 124 * q^26 - 34 * q^27 - 20 * q^28 + 48 * q^29 - 54 * q^30 - 72 * q^31 + 12 * q^32 + 52 * q^33 + 36 * q^34 - 34 * q^35 - 28 * q^36 + 24 * q^37 - 12 * q^38 + 20 * q^39 + 34 * q^40 - 144 * q^41 + 12 * q^42 - 4 * q^43 - 4 * q^44 + 56 * q^45 - 44 * q^46 - 48 * q^47 - 20 * q^48 - 50 * q^49 - 86 * q^50 - 106 * q^51 - 76 * q^52 - 12 * q^53 - 192 * q^54 - 110 * q^55 - 204 * q^56 - 88 * q^57 - 160 * q^58 - 76 * q^59 - 170 * q^60 + 8 * q^61 - 328 * q^62 - 164 * q^63 - 388 * q^64 - 190 * q^65 - 428 * q^66 - 212 * q^67 - 328 * q^68 - 16 * q^69 - 270 * q^70 - 168 * q^71 - 552 * q^72 - 286 * q^73 - 284 * q^74 + 44 * q^75 - 468 * q^76 - 76 * q^77 - 268 * q^78 - 128 * q^79 - 150 * q^80 - 384 * q^81 - 504 * q^82 - 24 * q^83 - 404 * q^84 - 4 * q^85 - 376 * q^86 - 156 * q^87 - 324 * q^88 - 208 * q^89 - 190 * q^90 - 220 * q^91 - 184 * q^92 - 36 * q^93 - 172 * q^94 - 6 * q^95 - 312 * q^96 + 28 * q^97 - 60 * q^98 + 98 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(760))\)

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
760.2.a	\(\chi_{760}(1, \cdot)\)	760.2.a.a	1	1
		760.2.a.b	1
		760.2.a.c	1
		760.2.a.d	1
		760.2.a.e	1
		760.2.a.f	2
		760.2.a.g	2
		760.2.a.h	3
		760.2.a.i	3
		760.2.a.j	3
760.2.d	\(\chi_{760}(609, \cdot)\)	760.2.d.a	2	1
		760.2.d.b	4
		760.2.d.c	4
		760.2.d.d	4
		760.2.d.e	12
760.2.e	\(\chi_{760}(531, \cdot)\)	760.2.e.a	80	1
760.2.f	\(\chi_{760}(381, \cdot)\)	760.2.f.a	28	1
		760.2.f.b	44
760.2.g	\(\chi_{760}(759, \cdot)\)	None	0	1
760.2.j	\(\chi_{760}(151, \cdot)\)	None	0	1
760.2.k	\(\chi_{760}(229, \cdot)\)	760.2.k.a	108	1
760.2.p	\(\chi_{760}(379, \cdot)\)	760.2.p.a	4	1
		760.2.p.b	4
		760.2.p.c	4
		760.2.p.d	8
		760.2.p.e	8
		760.2.p.f	8
		760.2.p.g	8
		760.2.p.h	16
		760.2.p.i	56
760.2.q	\(\chi_{760}(121, \cdot)\)	760.2.q.a	2	2
		760.2.q.b	2
		760.2.q.c	2
		760.2.q.d	8
		760.2.q.e	8
		760.2.q.f	8
		760.2.q.g	10
760.2.t	\(\chi_{760}(37, \cdot)\)	760.2.t.a	232	2
760.2.u	\(\chi_{760}(343, \cdot)\)	None	0	2
760.2.v	\(\chi_{760}(113, \cdot)\)	760.2.v.a	12	2
		760.2.v.b	48
760.2.w	\(\chi_{760}(267, \cdot)\)	760.2.w.a	2	2
		760.2.w.b	2
		760.2.w.c	104
		760.2.w.d	108
760.2.z	\(\chi_{760}(349, \cdot)\)	760.2.z.a	232	2
760.2.ba	\(\chi_{760}(31, \cdot)\)	None	0	2
760.2.bf	\(\chi_{760}(179, \cdot)\)	760.2.bf.a	8	2
		760.2.bf.b	224
760.2.bi	\(\chi_{760}(331, \cdot)\)	760.2.bi.a	160	2
760.2.bj	\(\chi_{760}(49, \cdot)\)	760.2.bj.a	4	2
		760.2.bj.b	56
760.2.bk	\(\chi_{760}(559, \cdot)\)	None	0	2
760.2.bl	\(\chi_{760}(501, \cdot)\)	760.2.bl.a	4	2
		760.2.bl.b	4
		760.2.bl.c	152
760.2.bo	\(\chi_{760}(81, \cdot)\)	760.2.bo.a	24	6
		760.2.bo.b	30
		760.2.bo.c	30
		760.2.bo.d	36
760.2.bp	\(\chi_{760}(293, \cdot)\)	760.2.bp.a	464	4
760.2.bq	\(\chi_{760}(7, \cdot)\)	None	0	4
760.2.bv	\(\chi_{760}(217, \cdot)\)	760.2.bv.a	120	4
760.2.bw	\(\chi_{760}(83, \cdot)\)	760.2.bw.a	8	4
		760.2.bw.b	456
760.2.bx	\(\chi_{760}(59, \cdot)\)	760.2.bx.a	24	6
		760.2.bx.b	672
760.2.cc	\(\chi_{760}(61, \cdot)\)	760.2.cc.a	480	6
760.2.cd	\(\chi_{760}(79, \cdot)\)	None	0	6
760.2.cg	\(\chi_{760}(9, \cdot)\)	760.2.cg.a	180	6
760.2.ch	\(\chi_{760}(51, \cdot)\)	760.2.ch.a	480	6
760.2.ci	\(\chi_{760}(71, \cdot)\)	None	0	6
760.2.cj	\(\chi_{760}(149, \cdot)\)	760.2.cj.a	696	6
760.2.co	\(\chi_{760}(33, \cdot)\)	760.2.co.a	360	12
760.2.cp	\(\chi_{760}(43, \cdot)\)	760.2.cp.a	1392	12
760.2.cs	\(\chi_{760}(13, \cdot)\)	760.2.cs.a	1392	12
760.2.ct	\(\chi_{760}(23, \cdot)\)	None	0	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(760)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 2}\)