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

• Label: 1800.3.cr
• Level: $1800$
• Weight: $3$
• Character orbit: 1800.cr
• Rep. character: $\chi_{1800}(37,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $2384$
• Sturm bound: $1080$

Defining parameters

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1800.cr (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
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	2416	3408
Cusp forms	5696	2384	3312
Eisenstein series	128	32	96

Trace form

2384 * q + 8 * q^2 - 10 * q^4 - 16 * q^7 + 2 * q^8 + 10 * q^14 - 6 * q^16 + 24 * q^17 - 34 * q^20 + 10 * q^22 + 16 * q^23 + 8 * q^25 + 16 * q^26 - 110 * q^28 - 12 * q^31 - 2 * q^32 - 10 * q^34 - 404 * q^38 + 420 * q^40 + 12 * q^41 + 360 * q^44 - 6 * q^46 - 176 * q^47 + 10 * q^50 - 436 * q^52 - 116 * q^55 + 6 * q^56 + 656 * q^58 + 484 * q^62 - 460 * q^64 + 72 * q^65 + 142 * q^68 + 106 * q^70 + 12 * q^71 + 104 * q^73 + 48 * q^76 - 20 * q^79 + 150 * q^80 + 386 * q^82 + 6 * q^86 + 1102 * q^88 - 980 * q^89 - 230 * q^92 - 410 * q^94 + 300 * q^95 - 216 * q^97 + 176 * q^98

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

\( S_{3}^{\mathrm{old}}(1800, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)