Space of modular forms of level 3000, weight 2, and Character 3000.cb

• Label: 3000.2.cb
• Level: $3000$
• Weight: $2$
• Character orbit: 3000.cb
• Rep. character: $\chi_{3000}(59,\cdot)$
• Character field: $\Q(\zeta_{50})$
• Dimension: $11920$
• Sturm bound: $1200$

Defining parameters

Level:	\( N \)	\(=\)	\( 3000 = 2^{3} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3000.cb (of order \(50\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3000 \)
Character field:			\(\Q(\zeta_{50})\)
Sturm bound:			\(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3000, [\chi])\).

	Total	New	Old
Modular forms	12080	12080	0
Cusp forms	11920	11920	0
Eisenstein series	160	160	0

Trace form

11920 * q - 40 * q^3 - 40 * q^4 - 20 * q^6 - 40 * q^9 - 40 * q^10 - 20 * q^12 - 20 * q^16 - 25 * q^18 - 80 * q^19 - 40 * q^22 - 15 * q^24 - 80 * q^25 - 40 * q^27 - 20 * q^30 - 40 * q^33 - 40 * q^34 - 220 * q^36 - 40 * q^40 - 40 * q^42 - 100 * q^43 - 40 * q^46 + 45 * q^48 - 2920 * q^49 - 30 * q^51 + 10 * q^52 - 85 * q^54 - 280 * q^58 - 5 * q^60 - 40 * q^64 - 95 * q^66 - 80 * q^67 + 30 * q^70 - 20 * q^72 - 80 * q^73 - 40 * q^75 - 30 * q^76 - 100 * q^78 - 40 * q^81 - 50 * q^82 + 15 * q^84 + 20 * q^88 - 45 * q^90 + 60 * q^91 + 100 * q^94 - 5 * q^96 - 40 * q^97 - 30 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3000, [\chi])\) into newform subspaces

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