Space of modular forms of level 640, weight 3, and Character 640.bk

• Label: 640.3.bk
• Level: $640$
• Weight: $3$
• Character orbit: 640.bk
• Rep. character: $\chi_{640}(13,\cdot)$
• Character field: $\Q(\zeta_{32})$
• Dimension: $3040$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	640.bk (of order \(32\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 640 \)
Character field:			\(\Q(\zeta_{32})\)
Sturm bound:			\(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(640, [\chi])\).

	Total	New	Old
Modular forms	3104	3104	0
Cusp forms	3040	3040	0
Eisenstein series	64	64	0

Trace form

3040 * q - 16 * q^2 - 16 * q^3 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^10 - 32 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^15 - 32 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^20 - 32 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^25 - 32 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^30 - 32 * q^31 - 16 * q^32 - 16 * q^35 - 32 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^40 - 32 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^45 - 32 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^50 - 32 * q^51 - 16 * q^52 - 16 * q^53 - 1040 * q^55 + 1312 * q^56 - 16 * q^57 - 16 * q^58 - 512 * q^59 - 16 * q^60 - 32 * q^61 + 48 * q^62 - 608 * q^66 - 16 * q^67 - 16 * q^68 - 16 * q^70 - 32 * q^71 - 16 * q^72 - 16 * q^73 - 1552 * q^75 - 1696 * q^76 - 16 * q^77 - 16 * q^78 - 1024 * q^79 - 16 * q^80 - 32 * q^81 + 2064 * q^82 - 16 * q^83 + 2464 * q^84 - 16 * q^85 - 32 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^90 - 32 * q^91 - 928 * q^92 - 160 * q^93 - 352 * q^94 - 16 * q^95 - 32 * q^96 - 16 * q^98 + 288 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(640, [\chi])\) into newform subspaces

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