Space of modular forms of level 800, weight 3, and Character 800.bw

• Label: 800.3.bw
• Level: $800$
• Weight: $3$
• Character orbit: 800.bw
• Rep. character: $\chi_{800}(13,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $3808$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	800.bw (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 800 \)
Character field:			\(\Q(\zeta_{40})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(800, [\chi])\).

	Total	New	Old
Modular forms	3872	3872	0
Cusp forms	3808	3808	0
Eisenstein series	64	64	0

Trace form

3808 * q - 16 * q^2 - 16 * q^3 - 20 * q^4 - 16 * q^5 - 12 * q^6 + 32 * q^8 - 20 * q^9 - 52 * q^10 - 12 * q^11 - 64 * q^12 - 16 * q^13 + 28 * q^14 - 12 * q^16 - 20 * q^19 - 100 * q^20 + 168 * q^21 + 96 * q^22 - 20 * q^23 - 16 * q^25 - 32 * q^26 - 52 * q^27 + 240 * q^28 - 20 * q^29 - 172 * q^30 - 24 * q^31 + 124 * q^32 - 32 * q^33 - 20 * q^34 + 480 * q^35 - 12 * q^36 - 16 * q^37 - 240 * q^38 - 20 * q^39 + 704 * q^40 - 12 * q^41 + 680 * q^42 + 112 * q^43 - 20 * q^44 - 16 * q^45 - 12 * q^46 + 64 * q^48 - 25312 * q^49 - 32 * q^50 - 32 * q^51 - 116 * q^52 - 16 * q^53 - 20 * q^54 - 272 * q^55 + 968 * q^56 + 336 * q^58 - 20 * q^59 + 48 * q^60 - 12 * q^61 + 252 * q^62 - 32 * q^63 + 880 * q^64 - 32 * q^65 + 1488 * q^66 + 1136 * q^67 + 356 * q^68 - 92 * q^69 + 1092 * q^70 - 12 * q^71 + 148 * q^72 - 20 * q^73 + 20 * q^75 - 32 * q^76 + 768 * q^77 + 476 * q^78 + 252 * q^80 + 400 * q^82 - 176 * q^83 + 568 * q^84 - 16 * q^85 - 12 * q^86 - 908 * q^87 - 348 * q^88 - 20 * q^89 - 1304 * q^90 + 968 * q^91 - 320 * q^92 + 20 * q^93 - 20 * q^94 - 32 * q^95 - 12 * q^96 - 32 * q^97 - 8 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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