Space of modular forms of level 448, weight 6, and Character 448.bm

• Label: 448.6.bm
• Level: $448$
• Weight: $6$
• Character orbit: 448.bm
• Rep. character: $\chi_{448}(3,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $5088$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	448.bm (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 448 \)
Character field:			\(\Q(\zeta_{48})\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(448, [\chi])\).

	Total	New	Old
Modular forms	5152	5152	0
Cusp forms	5088	5088	0
Eisenstein series	64	64	0

Trace form

5088 * q - 8 * q^2 - 24 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^7 - 32 * q^8 - 8 * q^9 - 24 * q^10 - 8 * q^11 - 24 * q^12 - 16 * q^14 - 32 * q^15 - 8 * q^16 - 24 * q^17 - 8 * q^18 - 24 * q^19 - 16 * q^21 - 27216 * q^22 - 8 * q^23 - 24 * q^24 - 8 * q^25 - 24 * q^26 - 4376 * q^28 - 32 * q^29 + 64872 * q^30 - 48 * q^31 - 8 * q^32 - 16 * q^35 + 124608 * q^36 - 8 * q^37 - 24 * q^38 - 8 * q^39 - 24 * q^40 - 46376 * q^42 - 32 * q^43 + 65504 * q^44 - 24 * q^45 - 8 * q^46 - 24 * q^47 - 16 * q^49 - 274160 * q^50 - 8 * q^51 - 220488 * q^52 - 8 * q^53 - 24 * q^54 - 16 * q^56 - 32 * q^57 - 8 * q^58 - 173784 * q^59 + 197848 * q^60 - 24 * q^61 - 749792 * q^64 - 16 * q^65 + 764616 * q^66 - 122328 * q^67 - 24 * q^68 - 16 * q^70 - 575392 * q^71 - 8 * q^72 - 24 * q^73 - 377728 * q^74 - 24 * q^75 - 16 * q^77 - 389696 * q^78 - 8 * q^79 + 1480368 * q^80 - 8 * q^81 + 1509336 * q^82 - 985056 * q^84 - 32 * q^85 - 8 * q^86 - 24 * q^87 - 8 * q^88 - 24 * q^89 - 16 * q^91 - 32 * q^92 - 3896 * q^93 - 24 * q^94 - 16 * q^95 - 3643056 * q^96 + 957288 * q^98 + 3856 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(448, [\chi])\) into newform subspaces

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