Space of modular forms of level 448, weight 8, and Character 448.bc

• Label: 448.8.bc
• Level: $448$
• Weight: $8$
• Character orbit: 448.bc
• Rep. character: $\chi_{448}(29,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $2688$
• Sturm bound: $512$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	448.bc (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 64 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(448, [\chi])\).

	Total	New	Old
Modular forms	3600	2688	912
Cusp forms	3568	2688	880
Eisenstein series	32	0	32

Trace form

2688 * q - 274456 * q^22 - 1455920 * q^26 + 1739920 * q^30 + 2142640 * q^32 - 806320 * q^34 - 4069520 * q^36 + 5372720 * q^40 - 3370472 * q^44 + 11973312 * q^51 + 2519424 * q^54 - 16764032 * q^55 + 10737272 * q^56 + 20716272 * q^58 - 4336416 * q^60 - 20695008 * q^62 + 20003760 * q^63 - 3881360 * q^67 + 17500128 * q^68 + 35990304 * q^70 + 45454608 * q^72 - 4214392 * q^74 + 45042048 * q^75 - 77885824 * q^76 - 78695184 * q^78 + 1047488 * q^79 + 93616000 * q^80 - 139071088 * q^86 - 105035680 * q^88 + 108881552 * q^92 + 149383104 * q^94

Decomposition of \(S_{8}^{\mathrm{new}}(448, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(448, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)