Space of modular forms of level 240 and weight 8

• Label: 240.8
• Level: 240
• Weight: 8
• Dimension: 4130
• Nonzero newspaces: 14
• Sturm bound: 24576
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 14 \)
Sturm bound:			\(24576\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(240))\).

	Total	New	Old
Modular forms	10976	4186	6790
Cusp forms	10528	4130	6398
Eisenstein series	448	56	392

Trace form

4130 * q + 52 * q^3 - 736 * q^4 + 278 * q^5 - 360 * q^6 + 644 * q^7 - 4008 * q^8 - 3498 * q^9 + 25936 * q^10 + 7224 * q^11 - 54712 * q^12 - 32272 * q^13 + 88056 * q^14 + 3696 * q^15 + 105536 * q^16 + 8724 * q^17 - 83176 * q^18 + 201448 * q^19 - 82000 * q^20 + 11076 * q^21 + 199552 * q^22 - 143416 * q^23 + 552736 * q^24 - 360582 * q^25 - 727960 * q^26 - 803480 * q^27 - 522000 * q^28 - 224220 * q^29 + 1519260 * q^30 + 1232952 * q^31 + 1000240 * q^32 - 524188 * q^33 - 3186336 * q^34 - 899184 * q^35 - 1811072 * q^36 + 2044568 * q^37 + 1353312 * q^38 + 253276 * q^39 + 7895048 * q^40 + 1967348 * q^41 + 5849200 * q^42 - 213004 * q^43 - 12168992 * q^44 - 2379410 * q^45 - 7634976 * q^46 - 1252248 * q^47 + 372856 * q^48 + 2228038 * q^49 + 11637632 * q^50 + 330816 * q^51 + 9060176 * q^52 - 1968932 * q^53 - 565104 * q^54 - 2249120 * q^55 - 19533696 * q^56 - 4903900 * q^57 - 6628768 * q^58 - 6279512 * q^59 + 5605408 * q^60 + 17309700 * q^61 + 29438088 * q^62 - 5727712 * q^63 + 21833888 * q^64 + 1629724 * q^65 - 29163176 * q^66 + 5312476 * q^67 - 38307216 * q^68 - 16594000 * q^69 + 25240200 * q^70 - 43160592 * q^71 + 50143208 * q^72 - 4472720 * q^73 - 1869960 * q^74 - 4314344 * q^75 + 11679872 * q^76 + 55133200 * q^77 - 2828912 * q^78 + 61157720 * q^79 - 49475752 * q^80 + 42126202 * q^81 - 7461216 * q^82 - 14254472 * q^83 + 43390528 * q^84 - 50438960 * q^85 + 15203296 * q^86 - 28292216 * q^87 - 65083232 * q^88 - 11685428 * q^89 + 11800712 * q^90 + 86410920 * q^91 - 40399888 * q^92 + 88644936 * q^93 + 87922736 * q^94 + 96733424 * q^95 + 66182944 * q^96 + 44207456 * q^97 + 164322944 * q^98 - 23595312 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(240))\)

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
240.8.a	\(\chi_{240}(1, \cdot)\)	240.8.a.a	1	1
		240.8.a.b	1
		240.8.a.c	1
		240.8.a.d	1
		240.8.a.e	1
		240.8.a.f	1
		240.8.a.g	1
		240.8.a.h	1
		240.8.a.i	1
		240.8.a.j	1
		240.8.a.k	1
		240.8.a.l	1
		240.8.a.m	1
		240.8.a.n	1
		240.8.a.o	2
		240.8.a.p	2
		240.8.a.q	2
		240.8.a.r	2
		240.8.a.s	2
		240.8.a.t	2
		240.8.a.u	2
240.8.b	\(\chi_{240}(71, \cdot)\)	None	0	1
240.8.d	\(\chi_{240}(169, \cdot)\)	None	0	1
240.8.f	\(\chi_{240}(49, \cdot)\)	240.8.f.a	2	1
		240.8.f.b	2
		240.8.f.c	4
		240.8.f.d	4
		240.8.f.e	8
		240.8.f.f	10
		240.8.f.g	12
240.8.h	\(\chi_{240}(191, \cdot)\)	240.8.h.a	20	1
		240.8.h.b	36
240.8.k	\(\chi_{240}(121, \cdot)\)	None	0	1
240.8.m	\(\chi_{240}(119, \cdot)\)	None	0	1
240.8.o	\(\chi_{240}(239, \cdot)\)	240.8.o.a	4	1
		240.8.o.b	24
		240.8.o.c	56
240.8.s	\(\chi_{240}(61, \cdot)\)	n/a	224	2
240.8.t	\(\chi_{240}(59, \cdot)\)	n/a	664	2
240.8.v	\(\chi_{240}(17, \cdot)\)	n/a	164	2
240.8.w	\(\chi_{240}(127, \cdot)\)	240.8.w.a	28	2
		240.8.w.b	56
240.8.y	\(\chi_{240}(163, \cdot)\)	n/a	336	2
240.8.bb	\(\chi_{240}(173, \cdot)\)	n/a	664	2
240.8.bc	\(\chi_{240}(43, \cdot)\)	n/a	336	2
240.8.bf	\(\chi_{240}(53, \cdot)\)	n/a	664	2
240.8.bh	\(\chi_{240}(7, \cdot)\)	None	0	2
240.8.bi	\(\chi_{240}(137, \cdot)\)	None	0	2
240.8.bk	\(\chi_{240}(11, \cdot)\)	n/a	448	2
240.8.bl	\(\chi_{240}(109, \cdot)\)	n/a	336	2

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(240))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(240)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 1}\)