Space of modular forms of level 448, weight 3, and Character 448.bf

• Label: 448.3.bf
• Level: $448$
• Weight: $3$
• Character orbit: 448.bf
• Rep. character: $\chi_{448}(13,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $1008$
• Sturm bound: $192$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.bf (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 448 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(448, [\chi])\).

	Total	New	Old
Modular forms	1040	1040	0
Cusp forms	1008	1008	0
Eisenstein series	32	32	0

Trace form

1008 * q - 16 * q^2 - 16 * q^4 - 8 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^11 - 8 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^18 - 8 * q^21 + 56 * q^22 - 16 * q^23 - 16 * q^25 - 128 * q^28 - 16 * q^29 + 64 * q^30 - 16 * q^32 - 8 * q^35 - 416 * q^36 - 16 * q^37 - 16 * q^39 + 432 * q^42 - 16 * q^43 - 120 * q^44 - 16 * q^46 - 8 * q^49 - 640 * q^50 - 16 * q^51 - 16 * q^53 - 8 * q^56 - 16 * q^57 - 16 * q^58 + 272 * q^60 - 16 * q^63 + 176 * q^64 - 32 * q^65 + 304 * q^67 - 8 * q^70 - 1040 * q^71 - 16 * q^72 - 632 * q^74 - 8 * q^77 + 1424 * q^78 - 16 * q^79 - 16 * q^81 + 1224 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^88 - 8 * q^91 - 16 * q^92 - 160 * q^93 - 416 * q^98 - 160 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(448, [\chi])\) into newform subspaces

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