Space of modular forms of level 640, weight 4, and Character 640.bl

• Label: 640.4.bl
• Level: $640$
• Weight: $4$
• Character orbit: 640.bl
• Rep. character: $\chi_{640}(3,\cdot)$
• Character field: $\Q(\zeta_{32})$
• Dimension: $4576$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	640.bl (of order \(32\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 640 \)
Character field:			\(\Q(\zeta_{32})\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(640, [\chi])\).

	Total	New	Old
Modular forms	4640	4640	0
Cusp forms	4576	4576	0
Eisenstein series	64	64	0

Trace form

4576 * 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 + 1136 * q^55 + 1312 * q^56 - 16 * q^57 - 16 * q^58 - 5504 * q^59 - 16 * q^60 - 32 * q^61 - 144 * q^62 - 32 * q^63 + 10912 * q^66 - 16 * q^67 - 16 * q^68 - 16 * q^70 - 32 * q^71 - 16 * q^72 - 16 * q^73 - 8848 * q^75 - 11936 * q^76 - 16 * q^77 - 16 * q^78 - 11328 * q^79 - 16 * q^80 - 32 * q^81 - 13936 * q^82 - 16 * q^83 - 8288 * q^84 - 16 * q^85 - 32 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^90 - 32 * q^91 - 25248 * q^92 + 416 * q^93 - 32736 * q^94 - 16 * q^95 - 32 * q^96 - 16 * q^98 + 864 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(640, [\chi])\) into newform subspaces

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