Space of modular forms of level 600, weight 3, and Character 600.bv

• Label: 600.3.bv
• Level: $600$
• Weight: $3$
• Character orbit: 600.bv
• Rep. character: $\chi_{600}(83,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1888$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	600.bv (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 600 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(600, [\chi])\).

	Total	New	Old
Modular forms	1952	1952	0
Cusp forms	1888	1888	0
Eisenstein series	64	64	0

Trace form

1888 * q - 16 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^9 - 24 * q^10 - 26 * q^12 - 12 * q^16 - 14 * q^18 - 40 * q^19 + 24 * q^22 - 32 * q^25 - 16 * q^27 + 32 * q^28 + 22 * q^30 - 52 * q^33 - 20 * q^34 - 70 * q^36 + 52 * q^40 - 614 * q^42 + 96 * q^43 - 12 * q^46 + 268 * q^48 - 32 * q^51 + 84 * q^52 + 640 * q^54 - 52 * q^57 - 184 * q^58 - 886 * q^60 - 20 * q^64 - 150 * q^66 - 32 * q^67 - 288 * q^70 + 70 * q^72 - 32 * q^73 + 208 * q^75 - 160 * q^76 - 264 * q^78 - 12 * q^81 + 436 * q^82 - 10 * q^84 + 840 * q^88 - 462 * q^90 - 24 * q^91 + 1380 * q^94 - 6 * q^96 + 96 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

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