Space of modular forms of level 256 and weight 12

• Label: 256.12
• Level: 256
• Weight: 12
• Dimension: 12620
• Nonzero newspaces: 6
• Sturm bound: 49152
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 256 = 2^{8} \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(49152\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(256))\).

	Total	New	Old
Modular forms	22704	12724	9980
Cusp forms	22352	12620	9732
Eisenstein series	352	104	248

Trace form

12620 * 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 - 1417208 * q^45 - 32 * q^46 - 24 * q^47 - 32 * q^48 - 7909307020 * q^49 - 32 * q^50 - 448885176 * q^51 - 32 * q^52 - 8402432256 * q^53 - 32 * q^54 + 38245610920 * q^55 - 32 * q^56 - 9050035432 * q^57 - 32 * q^58 - 45985560920 * q^59 - 32 * q^60 + 8603308064 * q^61 - 32 * q^62 + 79394923424 * q^63 - 32 * q^64 + 15079722232 * q^65 - 32 * q^66 - 101413780264 * q^67 - 32 * q^68 - 64773660128 * q^69 - 32 * q^70 + 87355804072 * q^71 - 32 * q^72 + 135658245912 * q^73 - 32 * q^74 - 112825763160 * q^75 - 32 * q^76 - 106666096128 * q^77 - 32 * q^78 + 219105923528 * q^79 - 32 * q^80 - 125524238484 * q^81 - 32 * q^82 - 24 * q^83 - 32 * q^84 - 390625032 * q^85 - 32 * q^86 - 24 * q^87 - 32 * q^88 - 40 * q^89 - 32 * q^90 - 24 * q^91 - 32 * q^92 + 2834320 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 56 * q^97 - 32 * q^98 - 1417200 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(256))\)

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
256.12.a	\(\chi_{256}(1, \cdot)\)	256.12.a.a	1	1
		256.12.a.b	1
		256.12.a.c	1
		256.12.a.d	1
		256.12.a.e	2
		256.12.a.f	2
		256.12.a.g	2
		256.12.a.h	4
		256.12.a.i	4
		256.12.a.j	6
		256.12.a.k	6
		256.12.a.l	8
		256.12.a.m	8
		256.12.a.n	8
		256.12.a.o	10
		256.12.a.p	10
		256.12.a.q	12
256.12.b	\(\chi_{256}(129, \cdot)\)	256.12.b.a	2	1
		256.12.b.b	2
		256.12.b.c	2
		256.12.b.d	2
		256.12.b.e	2
		256.12.b.f	2
		256.12.b.g	2
		256.12.b.h	4
		256.12.b.i	4
		256.12.b.j	4
		256.12.b.k	4
		256.12.b.l	6
		256.12.b.m	6
		256.12.b.n	10
		256.12.b.o	10
		256.12.b.p	12
		256.12.b.q	12
256.12.e	\(\chi_{256}(65, \cdot)\)	n/a	176	2
256.12.g	\(\chi_{256}(33, \cdot)\)	n/a	344	4
256.12.i	\(\chi_{256}(17, \cdot)\)	n/a	696	8
256.12.k	\(\chi_{256}(9, \cdot)\)	None	0	16
256.12.m	\(\chi_{256}(5, \cdot)\)	n/a	11232	32

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

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(256))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(256)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 7}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)