Space of modular forms of level 256 and weight 4

• Label: 256.4
• Level: 256
• Weight: 4
• Dimension: 3404
• Nonzero newspaces: 6
• Sturm bound: 16384
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 256 = 2^{8} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(16384\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(256))\).

	Total	New	Old
Modular forms	6320	3508	2812
Cusp forms	5968	3404	2564
Eisenstein series	352	104	248

Trace form

3404 * 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 - 248 * q^45 - 32 * q^46 - 24 * q^47 - 32 * q^48 - 1420 * q^49 - 32 * q^50 - 3000 * q^51 - 32 * q^52 - 1536 * q^53 - 32 * q^54 - 600 * q^55 - 32 * q^56 + 1304 * q^57 - 32 * q^58 + 2728 * q^59 - 32 * q^60 + 3616 * q^61 - 32 * q^62 + 5024 * q^63 - 32 * q^64 + 3832 * q^65 - 32 * q^66 + 4056 * q^67 - 32 * q^68 + 2080 * q^69 - 32 * q^70 + 424 * q^71 - 32 * q^72 - 1768 * q^73 - 32 * q^74 - 4440 * q^75 - 32 * q^76 - 3840 * q^77 - 32 * q^78 - 5688 * q^79 - 32 * q^80 - 2964 * q^81 - 32 * q^82 - 24 * q^83 - 32 * q^84 - 1032 * q^85 - 32 * q^86 - 24 * q^87 - 32 * q^88 - 40 * q^89 - 32 * q^90 - 24 * q^91 - 32 * q^92 + 400 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 56 * q^97 - 32 * q^98 - 240 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(256))\)

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
256.4.a	\(\chi_{256}(1, \cdot)\)	256.4.a.a	1	1
		256.4.a.b	1
		256.4.a.c	1
		256.4.a.d	1
		256.4.a.e	1
		256.4.a.f	1
		256.4.a.g	1
		256.4.a.h	1
		256.4.a.i	2
		256.4.a.j	2
		256.4.a.k	2
		256.4.a.l	2
		256.4.a.m	2
		256.4.a.n	4
256.4.b	\(\chi_{256}(129, \cdot)\)	256.4.b.a	2	1
		256.4.b.b	2
		256.4.b.c	2
		256.4.b.d	2
		256.4.b.e	2
		256.4.b.f	2
		256.4.b.g	2
		256.4.b.h	4
		256.4.b.i	4
256.4.e	\(\chi_{256}(65, \cdot)\)	256.4.e.a	8	2
		256.4.e.b	8
		256.4.e.c	16
		256.4.e.d	16
256.4.g	\(\chi_{256}(33, \cdot)\)	256.4.g.a	44	4
		256.4.g.b	44
256.4.i	\(\chi_{256}(17, \cdot)\)	n/a	184	8
256.4.k	\(\chi_{256}(9, \cdot)\)	None	0	16
256.4.m	\(\chi_{256}(5, \cdot)\)	n/a	3040	32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(256))\) into lower level spaces

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