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

• Label: 1800.3.bx
• Level: $1800$
• Weight: $3$
• Character orbit: 1800.bx
• Rep. character: $\chi_{1800}(19,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $1192$
• Sturm bound: $1080$

Defining parameters

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1800.bx (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(1080\)

Dimensions

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

	Total	New	Old
Modular forms	2912	1208	1704
Cusp forms	2848	1192	1656
Eisenstein series	64	16	48

Trace form

1192 * q + 5 * q^2 - 3 * q^4 + 20 * q^8 - 13 * q^10 + 6 * q^11 + 45 * q^14 + 57 * q^16 + 10 * q^17 - 6 * q^19 - 27 * q^20 - 80 * q^22 - 20 * q^25 + 50 * q^26 - 85 * q^28 + 69 * q^34 + 256 * q^35 + 485 * q^38 - 290 * q^40 - 34 * q^41 - 134 * q^44 + 105 * q^46 + 7992 * q^49 - 181 * q^50 - 220 * q^52 + 240 * q^56 - 380 * q^58 + 6 * q^59 - 320 * q^62 + 252 * q^64 + 66 * q^65 - 730 * q^67 + 18 * q^70 - 10 * q^73 + 100 * q^74 - 156 * q^76 - 108 * q^80 + 10 * q^83 + 441 * q^86 + 1150 * q^88 + 306 * q^89 - 300 * q^91 + 240 * q^92 + 85 * q^94 + 70 * q^97 + 200 * 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

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