Space of modular forms of level 256 and weight 6

• Label: 256.6
• Level: 256
• Weight: 6
• Dimension: 5708
• Nonzero newspaces: 6
• Sturm bound: 24576
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 256 = 2^{8} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(24576\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(256))\).

	Total	New	Old
Modular forms	10416	5812	4604
Cusp forms	10064	5708	4356
Eisenstein series	352	104	248

Trace form

5708 * 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 - 1976 * q^45 - 32 * q^46 - 24 * q^47 - 32 * q^48 - 67276 * q^49 - 32 * q^50 - 41784 * q^51 - 32 * q^52 + 98880 * q^53 - 32 * q^54 + 220072 * q^55 - 32 * q^56 + 103064 * q^57 - 32 * q^58 - 57944 * q^59 - 32 * q^60 - 192352 * q^61 - 32 * q^62 - 317536 * q^63 - 32 * q^64 - 221576 * q^65 - 32 * q^66 - 122344 * q^67 - 32 * q^68 + 89248 * q^69 - 32 * q^70 + 287656 * q^71 - 32 * q^72 + 420504 * q^73 - 32 * q^74 + 386472 * q^75 - 32 * q^76 + 29760 * q^77 - 32 * q^78 - 355384 * q^79 - 32 * q^80 - 236244 * q^81 - 32 * q^82 - 24 * q^83 - 32 * q^84 - 25032 * q^85 - 32 * q^86 - 24 * q^87 - 32 * q^88 - 40 * q^89 - 32 * q^90 - 24 * q^91 - 32 * q^92 + 3856 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 56 * q^97 - 32 * q^98 - 1968 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(256))\)

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
256.6.a	\(\chi_{256}(1, \cdot)\)	256.6.a.a	1	1
		256.6.a.b	1
		256.6.a.c	1
		256.6.a.d	1
		256.6.a.e	2
		256.6.a.f	2
		256.6.a.g	2
		256.6.a.h	2
		256.6.a.i	2
		256.6.a.j	4
		256.6.a.k	4
		256.6.a.l	4
		256.6.a.m	4
		256.6.a.n	4
		256.6.a.o	4
256.6.b	\(\chi_{256}(129, \cdot)\)	256.6.b.a	2	1
		256.6.b.b	2
		256.6.b.c	2
		256.6.b.d	2
		256.6.b.e	2
		256.6.b.f	2
		256.6.b.g	2
		256.6.b.h	2
		256.6.b.i	2
		256.6.b.j	4
		256.6.b.k	4
		256.6.b.l	4
		256.6.b.m	4
		256.6.b.n	4
256.6.e	\(\chi_{256}(65, \cdot)\)	256.6.e.a	16	2
		256.6.e.b	16
		256.6.e.c	24
		256.6.e.d	24
256.6.g	\(\chi_{256}(33, \cdot)\)	n/a	152	4
256.6.i	\(\chi_{256}(17, \cdot)\)	n/a	312	8
256.6.k	\(\chi_{256}(9, \cdot)\)	None	0	16
256.6.m	\(\chi_{256}(5, \cdot)\)	n/a	5088	32

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(256))\) into lower level spaces

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