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

• Label: 800.3.bz
• Level: $800$
• Weight: $3$
• Character orbit: 800.bz
• Rep. character: $\chi_{800}(19,\cdot)$
• 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.bz (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 - 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 - 32 * q^15 - 12 * q^16 - 12 * q^19 - 16 * q^20 - 12 * q^21 - 20 * q^22 - 20 * q^23 - 32 * q^24 - 16 * q^25 + 168 * q^26 - 20 * q^27 - 20 * q^28 - 12 * q^29 - 72 * q^30 - 40 * q^33 + 20 * q^34 - 112 * q^35 + 588 * q^36 - 20 * q^37 + 1240 * q^38 - 12 * q^39 - 960 * q^40 - 12 * q^41 - 20 * q^42 - 12 * q^44 - 52 * q^45 - 12 * q^46 - 40 * q^47 + 240 * q^48 + 296 * q^50 + 40 * q^51 - 20 * q^52 - 20 * q^53 - 12 * q^54 + 240 * q^55 - 12 * q^56 - 20 * q^58 - 12 * q^59 - 1264 * q^60 - 12 * q^61 - 20 * q^62 - 552 * q^64 - 32 * q^65 - 44 * q^66 - 20 * q^67 - 12 * q^69 - 28 * q^70 - 12 * q^71 - 20 * q^72 - 20 * q^73 + 408 * q^74 - 400 * q^75 - 32 * q^76 - 20 * q^77 - 20 * q^78 - 24 * q^79 - 260 * q^80 - 20 * q^83 - 772 * q^84 + 84 * q^85 - 12 * q^86 - 20 * q^87 - 2000 * q^88 - 12 * q^89 - 532 * q^90 - 12 * q^91 - 2360 * q^92 - 844 * q^94 + 1788 * q^96 - 40 * q^97 + 60 * q^98 - 104 * q^99

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

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