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

• Label: 1200.3.cr
• Level: $1200$
• Weight: $3$
• Character orbit: 1200.cr
• Rep. character: $\chi_{1200}(13,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1920$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1200.cr (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 400 \)
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	1920	1952
Cusp forms	3808	1920	1888
Eisenstein series	64	0	64

Trace form

1920 * q - 12 * q^8 + 1440 * q^9 - 24 * q^12 + 200 * q^16 + 84 * q^20 - 184 * q^22 + 124 * q^28 - 264 * q^30 - 140 * q^32 + 96 * q^35 - 160 * q^38 - 784 * q^40 + 60 * q^42 + 128 * q^43 + 700 * q^44 + 144 * q^48 + 1004 * q^50 + 232 * q^52 + 20 * q^58 - 512 * q^62 + 900 * q^64 + 864 * q^67 + 264 * q^68 - 4 * q^70 - 144 * q^72 + 96 * q^73 + 192 * q^75 + 216 * q^78 + 324 * q^80 - 4320 * q^81 + 248 * q^82 + 1000 * q^86 - 668 * q^88 - 528 * q^92 + 768 * q^95 - 656 * q^98

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

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

Decomposition of \(S_{3}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1200, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)