Space of modular forms of level 1800, weight 3, and Character 1800.cu

• Label: 1800.3.cu
• Level: $1800$
• Weight: $3$
• Character orbit: 1800.cu
• Rep. character: $\chi_{1800}(323,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1920$
• Sturm bound: $1080$

Defining parameters

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1800.cu (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 600 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1800, [\chi])\).

	Total	New	Old
Modular forms	5824	1920	3904
Cusp forms	5696	1920	3776
Eisenstein series	128	0	128

Trace form

\( 1920 q + 16 q^{10} - 112 q^{22} + 32 q^{28} - 136 q^{40} - 256 q^{43} - 72 q^{52} + 304 q^{58} + 416 q^{70} - 1440 q^{82} - 2128 q^{88} - 400 q^{94} - 256 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1800, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)