Space of modular forms of level 4000, weight 2, and Character 4000.df

• Label: 4000.2.df
• Level: $4000$
• Weight: $2$
• Character orbit: 4000.df
• Rep. character: $\chi_{4000}(67,\cdot)$
• Character field: $\Q(\zeta_{200})$
• Dimension: $47840$
• Sturm bound: $1200$

Defining parameters

Level:	\( N \)	\(=\)	\( 4000 = 2^{5} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4000.df (of order \(200\) and degree \(80\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4000 \)
Character field:			\(\Q(\zeta_{200})\)
Sturm bound:			\(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4000, [\chi])\).

	Total	New	Old
Modular forms	48160	48160	0
Cusp forms	47840	47840	0
Eisenstein series	320	320	0

Trace form

47840 * q - 80 * q^2 - 80 * q^3 - 80 * q^4 - 80 * q^5 - 80 * q^6 - 100 * q^7 - 20 * q^8 - 80 * q^9 - 80 * q^10 - 80 * q^11 - 80 * q^12 - 80 * q^13 - 120 * q^14 - 160 * q^15 - 80 * q^16 - 80 * q^18 - 80 * q^19 - 80 * q^20 - 140 * q^21 - 80 * q^22 - 80 * q^23 - 100 * q^24 - 80 * q^25 - 60 * q^26 - 80 * q^27 - 160 * q^28 - 80 * q^29 - 80 * q^30 - 80 * q^32 - 160 * q^33 - 80 * q^34 - 180 * q^35 - 80 * q^36 - 80 * q^37 - 80 * q^38 - 80 * q^39 - 180 * q^40 - 80 * q^41 - 200 * q^42 - 80 * q^43 - 80 * q^44 - 80 * q^45 - 80 * q^46 - 160 * q^47 + 180 * q^48 + 11720 * q^49 - 80 * q^50 - 60 * q^51 - 80 * q^52 - 80 * q^53 - 80 * q^54 - 80 * q^55 - 220 * q^56 - 160 * q^57 - 80 * q^58 - 80 * q^59 - 80 * q^60 - 80 * q^61 - 80 * q^62 - 280 * q^63 - 20 * q^64 - 160 * q^65 - 380 * q^66 + 400 * q^67 - 80 * q^68 - 80 * q^69 - 220 * q^70 - 80 * q^71 - 80 * q^72 - 80 * q^73 - 100 * q^74 - 80 * q^75 - 60 * q^76 - 220 * q^77 - 80 * q^78 - 160 * q^79 - 80 * q^80 - 80 * q^82 - 80 * q^83 - 220 * q^84 - 80 * q^85 - 80 * q^86 - 80 * q^87 - 80 * q^88 - 80 * q^89 - 80 * q^90 - 220 * q^91 - 80 * q^92 - 80 * q^93 - 80 * q^94 - 80 * q^96 - 160 * q^97 - 180 * q^98 - 100 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(4000, [\chi])\) into newform subspaces

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