Space of modular forms of level 256 and weight 8

• Label: 256.8
• Level: 256
• Weight: 8
• Dimension: 8012
• Nonzero newspaces: 6
• Sturm bound: 32768
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 256 = 2^{8} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(32768\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(256))\).

	Total	New	Old
Modular forms	14512	8116	6396
Cusp forms	14160	8012	6148
Eisenstein series	352	104	248

Trace form

8012 * q - 32 * q^2 - 24 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 24 * q^7 - 32 * q^8 - 40 * q^9 - 32 * q^10 - 24 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 24 * q^15 - 32 * q^16 - 48 * q^17 - 32 * q^18 - 24 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 24 * q^23 - 32 * q^24 - 40 * q^25 - 32 * q^26 - 24 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 56 * q^33 - 32 * q^34 - 24 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 24 * q^39 - 32 * q^40 - 40 * q^41 - 32 * q^42 - 24 * q^43 - 32 * q^44 - 17528 * q^45 - 32 * q^46 - 24 * q^47 - 32 * q^48 - 3294220 * q^49 - 32 * q^50 + 5986632 * q^51 - 32 * q^52 + 3631232 * q^53 - 32 * q^54 - 8382040 * q^55 - 32 * q^56 - 12408808 * q^57 - 32 * q^58 - 3671896 * q^59 - 32 * q^60 + 9119520 * q^61 - 32 * q^62 + 20003744 * q^63 - 32 * q^64 + 11415032 * q^65 - 32 * q^66 - 3881384 * q^67 - 32 * q^68 - 19161824 * q^69 - 32 * q^70 - 24697432 * q^71 - 32 * q^72 - 10136552 * q^73 - 32 * q^74 + 22521000 * q^75 - 32 * q^76 + 23828864 * q^77 - 32 * q^78 + 523720 * q^79 - 32 * q^80 - 19131924 * q^81 - 32 * q^82 - 24 * q^83 - 32 * q^84 - 625032 * q^85 - 32 * q^86 - 24 * q^87 - 32 * q^88 - 40 * q^89 - 32 * q^90 - 24 * q^91 - 32 * q^92 + 34960 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 56 * q^97 - 32 * q^98 - 17520 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(256))\)

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
256.8.a	\(\chi_{256}(1, \cdot)\)	256.8.a.a	1	1
		256.8.a.b	1
		256.8.a.c	1
		256.8.a.d	1
		256.8.a.e	2
		256.8.a.f	2
		256.8.a.g	2
		256.8.a.h	2
		256.8.a.i	2
		256.8.a.j	4
		256.8.a.k	4
		256.8.a.l	4
		256.8.a.m	4
		256.8.a.n	4
		256.8.a.o	4
		256.8.a.p	4
		256.8.a.q	6
		256.8.a.r	6
256.8.b	\(\chi_{256}(129, \cdot)\)	256.8.b.a	2	1
		256.8.b.b	2
		256.8.b.c	2
		256.8.b.d	2
		256.8.b.e	2
		256.8.b.f	2
		256.8.b.g	2
		256.8.b.h	4
		256.8.b.i	4
		256.8.b.j	4
		256.8.b.k	6
		256.8.b.l	6
		256.8.b.m	8
		256.8.b.n	8
256.8.e	\(\chi_{256}(65, \cdot)\)	n/a	112	2
256.8.g	\(\chi_{256}(33, \cdot)\)	n/a	216	4
256.8.i	\(\chi_{256}(17, \cdot)\)	n/a	440	8
256.8.k	\(\chi_{256}(9, \cdot)\)	None	0	16
256.8.m	\(\chi_{256}(5, \cdot)\)	n/a	7136	32

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(256))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(256)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 7}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)