Space of modular forms of level 360 and weight 4

• Label: 360.4
• Level: 360
• Weight: 4
• Dimension: 4177
• Nonzero newspaces: 18
• Sturm bound: 27648
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(27648\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(360))\).

	Total	New	Old
Modular forms	10752	4285	6467
Cusp forms	9984	4177	5807
Eisenstein series	768	108	660

Trace form

4177 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 + 11 * q^5 + 8 * q^6 + 84 * q^7 - 64 * q^8 - 74 * q^9 - 116 * q^10 - 210 * q^11 - 228 * q^12 - 74 * q^13 - 172 * q^14 - 40 * q^15 - 404 * q^16 + 174 * q^17 + 224 * q^18 + 112 * q^19 + 62 * q^20 - 112 * q^21 + 972 * q^22 - 276 * q^23 + 512 * q^24 - 1091 * q^25 + 280 * q^26 - 1144 * q^27 + 648 * q^28 - 234 * q^29 - 134 * q^30 - 80 * q^31 - 684 * q^32 + 498 * q^33 - 2488 * q^34 + 12 * q^35 + 1500 * q^36 + 382 * q^37 + 140 * q^38 + 1512 * q^39 + 738 * q^40 + 1908 * q^41 + 4 * q^42 + 2194 * q^43 + 1828 * q^44 - 446 * q^45 + 2272 * q^46 - 100 * q^47 - 2512 * q^48 - 2213 * q^49 - 1534 * q^50 - 1346 * q^51 + 1600 * q^52 - 2506 * q^53 + 1752 * q^54 + 1060 * q^55 + 2624 * q^56 - 562 * q^57 - 1400 * q^58 - 3006 * q^59 + 6266 * q^60 + 338 * q^61 + 928 * q^62 + 1000 * q^63 - 152 * q^64 + 4048 * q^65 - 3128 * q^66 + 990 * q^67 + 196 * q^68 + 6676 * q^69 - 126 * q^70 + 7544 * q^71 - 9684 * q^72 - 1810 * q^73 - 7544 * q^74 - 3914 * q^75 + 4 * q^76 - 1416 * q^77 - 9572 * q^78 - 4280 * q^79 - 6512 * q^80 - 2850 * q^81 - 11644 * q^82 - 8084 * q^83 - 832 * q^84 - 4226 * q^85 + 4852 * q^86 - 7692 * q^87 - 6980 * q^88 - 2342 * q^89 - 1886 * q^90 - 864 * q^91 - 1828 * q^92 - 100 * q^93 + 2008 * q^94 + 468 * q^95 + 8032 * q^96 + 628 * q^97 + 16168 * q^98 + 8988 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(360))\)

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
360.4.a	\(\chi_{360}(1, \cdot)\)	360.4.a.a	1	1
		360.4.a.b	1
		360.4.a.c	1
		360.4.a.d	1
		360.4.a.e	1
		360.4.a.f	1
		360.4.a.g	1
		360.4.a.h	1
		360.4.a.i	1
		360.4.a.j	1
		360.4.a.k	1
		360.4.a.l	1
		360.4.a.m	1
		360.4.a.n	1
		360.4.a.o	1
360.4.b	\(\chi_{360}(251, \cdot)\)	360.4.b.a	24	1
		360.4.b.b	24
360.4.d	\(\chi_{360}(109, \cdot)\)	360.4.d.a	4	1
		360.4.d.b	4
		360.4.d.c	4
		360.4.d.d	16
		360.4.d.e	18
		360.4.d.f	18
		360.4.d.g	24
360.4.f	\(\chi_{360}(289, \cdot)\)	360.4.f.a	2	1
		360.4.f.b	2
		360.4.f.c	2
		360.4.f.d	4
		360.4.f.e	4
		360.4.f.f	8
360.4.h	\(\chi_{360}(71, \cdot)\)	None	0	1
360.4.k	\(\chi_{360}(181, \cdot)\)	360.4.k.a	2	1
		360.4.k.b	8
		360.4.k.c	12
		360.4.k.d	14
		360.4.k.e	24
360.4.m	\(\chi_{360}(179, \cdot)\)	360.4.m.a	4	1
		360.4.m.b	4
		360.4.m.c	64
360.4.o	\(\chi_{360}(359, \cdot)\)	None	0	1
360.4.q	\(\chi_{360}(121, \cdot)\)	360.4.q.a	2	2
		360.4.q.b	16
		360.4.q.c	16
		360.4.q.d	18
		360.4.q.e	20
360.4.s	\(\chi_{360}(17, \cdot)\)	360.4.s.a	4	2
		360.4.s.b	16
		360.4.s.c	16
360.4.t	\(\chi_{360}(127, \cdot)\)	None	0	2
360.4.w	\(\chi_{360}(163, \cdot)\)	n/a	176	2
360.4.x	\(\chi_{360}(53, \cdot)\)	n/a	144	2
360.4.bb	\(\chi_{360}(119, \cdot)\)	None	0	2
360.4.bd	\(\chi_{360}(59, \cdot)\)	n/a	424	2
360.4.bf	\(\chi_{360}(61, \cdot)\)	n/a	288	2
360.4.bg	\(\chi_{360}(191, \cdot)\)	None	0	2
360.4.bi	\(\chi_{360}(49, \cdot)\)	n/a	108	2
360.4.bk	\(\chi_{360}(229, \cdot)\)	n/a	424	2
360.4.bm	\(\chi_{360}(11, \cdot)\)	n/a	288	2
360.4.bo	\(\chi_{360}(43, \cdot)\)	n/a	848	4
360.4.br	\(\chi_{360}(77, \cdot)\)	n/a	848	4
360.4.bs	\(\chi_{360}(113, \cdot)\)	n/a	216	4
360.4.bv	\(\chi_{360}(7, \cdot)\)	None	0	4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(360))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(360)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 1}\)