Space of modular forms of level 256 and weight 9

• Label: 256.9
• Level: 256
• Weight: 9
• Dimension: 9164
• Nonzero newspaces: 6
• Sturm bound: 36864
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 256 = 2^{8} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(36864\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(256))\).

	Total	New	Old
Modular forms	16560	9268	7292
Cusp forms	16208	9164	7044
Eisenstein series	352	104	248

Trace form

9164 * 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 - 16 * 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 + 52456 * q^45 - 32 * q^46 - 24 * q^47 - 32 * q^48 + 23059156 * q^49 - 32 * q^50 - 55448088 * q^51 - 32 * q^52 + 10717408 * q^53 - 32 * q^54 + 92653544 * q^55 - 32 * q^56 + 12400088 * q^57 - 32 * q^58 - 89877528 * q^59 - 32 * q^60 - 97904160 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 + 119766456 * q^65 - 32 * q^66 + 186760936 * q^67 - 32 * q^68 + 34546144 * q^69 - 32 * q^70 - 159664152 * q^71 - 32 * q^72 - 251476520 * q^73 - 32 * q^74 - 51674136 * q^75 - 32 * q^76 + 189928672 * q^77 - 32 * q^78 + 144406504 * q^79 - 32 * q^80 - 172186932 * q^81 - 32 * q^82 - 24 * q^83 - 32 * q^84 - 3125032 * q^85 - 32 * q^86 - 24 * q^87 - 32 * q^88 - 40 * q^89 - 32 * q^90 - 24 * q^91 - 32 * q^92 - 105008 * q^93 - 32 * q^94 - 16 * q^95 - 32 * q^96 - 56 * q^97 - 32 * q^98 - 52512 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(256))\)

We only show spaces with odd 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
256.9.c	\(\chi_{256}(255, \cdot)\)	256.9.c.a	1	1
		256.9.c.b	1
		256.9.c.c	2
		256.9.c.d	2
		256.9.c.e	2
		256.9.c.f	2
		256.9.c.g	2
		256.9.c.h	2
		256.9.c.i	4
		256.9.c.j	4
		256.9.c.k	8
		256.9.c.l	8
		256.9.c.m	12
		256.9.c.n	12
256.9.d	\(\chi_{256}(127, \cdot)\)	256.9.d.a	2	1
		256.9.d.b	4
		256.9.d.c	4
		256.9.d.d	4
		256.9.d.e	4
		256.9.d.f	4
		256.9.d.g	4
		256.9.d.h	4
		256.9.d.i	16
		256.9.d.j	16
256.9.f	\(\chi_{256}(63, \cdot)\)	n/a	128	2
256.9.h	\(\chi_{256}(31, \cdot)\)	n/a	248	4
256.9.j	\(\chi_{256}(15, \cdot)\)	n/a	504	8
256.9.l	\(\chi_{256}(7, \cdot)\)	None	0	16
256.9.n	\(\chi_{256}(3, \cdot)\)	n/a	8160	32

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(256))\) into lower level spaces

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