Space of modular forms of level 256, weight 8, and Character 256.i

• Label: 256.8.i
• Level: $256$
• Weight: $8$
• Character orbit: 256.i
• Rep. character: $\chi_{256}(17,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $440$
• Sturm bound: $256$

Defining parameters

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	256.i (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 64 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(256\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(256, [\chi])\).

	Total	New	Old
Modular forms	1824	456	1368
Cusp forms	1760	440	1320
Eisenstein series	64	16	48

Trace form

440 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 + 5986664 * q^51 - 8 * q^53 - 8382008 * q^55 - 8 * q^57 - 3671864 * q^59 - 8 * q^61 + 20003776 * q^63 - 16 * q^65 - 3881352 * q^67 - 8 * q^69 - 24697400 * q^71 - 8 * q^73 + 22521032 * q^75 - 8 * q^77 + 523752 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 17488 * q^93 - 17488 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(256, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{8}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(256, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)