Space of modular forms of level 1200, weight 3, and Character 1200.cg

• Label: 1200.3.cg
• Level: $1200$
• Weight: $3$
• Character orbit: 1200.cg
• Rep. character: $\chi_{1200}(221,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $3808$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1200.cg (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1200 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1200, [\chi])\).

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

Trace form

3808 * q - 6 * q^3 - 12 * q^4 - 6 * q^6 - 16 * q^10 - 6 * q^12 - 12 * q^13 - 16 * q^15 - 12 * q^16 - 12 * q^19 + 48 * q^21 - 124 * q^22 - 16 * q^24 - 6 * q^27 + 180 * q^28 - 94 * q^30 - 24 * q^31 - 12 * q^33 - 204 * q^34 + 230 * q^36 - 12 * q^37 - 108 * q^40 + 210 * q^42 + 96 * q^43 + 42 * q^45 + 20 * q^46 - 84 * q^48 - 25376 * q^49 - 52 * q^51 + 196 * q^52 - 6 * q^54 + 340 * q^58 - 1584 * q^60 - 12 * q^61 + 576 * q^63 - 12 * q^64 - 472 * q^66 - 12 * q^67 + 30 * q^69 + 648 * q^70 + 670 * q^72 - 138 * q^75 - 512 * q^76 + 86 * q^78 - 24 * q^79 - 12 * q^81 - 520 * q^82 - 92 * q^84 - 116 * q^85 + 100 * q^88 - 838 * q^90 + 576 * q^91 + 20 * q^93 - 64 * q^94 - 6 * q^96 - 24 * q^97 + 308 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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