Space of modular forms of level 800, weight 6, and Character 800.by

• Label: 800.6.by
• Level: $800$
• Weight: $6$
• Character orbit: 800.by
• Rep. character: $\chi_{800}(29,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $9568$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	800.by (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 800 \)
Character field:			\(\Q(\zeta_{40})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(800, [\chi])\).

	Total	New	Old
Modular forms	9632	9632	0
Cusp forms	9568	9568	0
Eisenstein series	64	64	0

Trace form

9568 * q - 20 * q^2 - 20 * q^3 - 12 * q^4 - 16 * q^5 - 12 * q^6 - 20 * q^8 - 12 * q^9 - 16 * q^10 - 12 * q^11 - 20 * q^12 - 20 * q^13 - 12 * q^14 - 12 * q^16 - 12 * q^19 - 16 * q^20 - 12 * q^21 - 20 * q^22 - 20 * q^23 - 32 * q^24 - 16 * q^25 + 25928 * q^26 - 20 * q^27 - 20 * q^28 - 12 * q^29 + 32552 * q^30 + 46104 * q^31 - 40 * q^33 + 244 * q^34 + 4760 * q^35 - 93492 * q^36 - 20 * q^37 + 172040 * q^38 - 12 * q^39 + 64576 * q^40 - 12 * q^41 - 20 * q^42 - 12 * q^44 + 956 * q^45 - 12 * q^46 + 561840 * q^48 - 4536 * q^50 + 1912 * q^51 - 20 * q^52 - 20 * q^53 - 12 * q^54 + 110032 * q^55 - 12 * q^56 - 20 * q^58 - 12 * q^59 - 298032 * q^60 - 12 * q^61 - 20 * q^62 - 40 * q^63 + 414744 * q^64 - 32 * q^65 - 268 * q^66 - 20 * q^67 - 12 * q^69 + 343220 * q^70 - 12 * q^71 - 20 * q^72 - 20 * q^73 - 48520 * q^74 + 193232 * q^75 - 32 * q^76 - 20 * q^77 - 20 * q^78 - 493188 * q^80 - 20 * q^83 - 209924 * q^84 + 12484 * q^85 - 12 * q^86 - 20 * q^87 + 1557360 * q^88 - 12 * q^89 + 564620 * q^90 - 12 * q^91 + 1731400 * q^92 - 118572 * q^94 - 32 * q^95 + 595068 * q^96 - 40 * q^97 + 620 * q^98 - 1976 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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