Space of modular forms of level 1800, weight 4, and Character 1800.cp

• Label: 1800.4.cp
• Level: $1800$
• Weight: $4$
• Character orbit: 1800.cp
• Rep. character: $\chi_{1800}(163,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $3584$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1800.cp (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).

	Total	New	Old
Modular forms	8704	3616	5088
Cusp forms	8576	3584	4992
Eisenstein series	128	32	96

Trace form

3584 * q + 8 * q^2 - 10 * q^4 + 50 * q^8 + 64 * q^10 + 12 * q^11 + 10 * q^14 - 6 * q^16 - 36 * q^17 - 20 * q^19 + 70 * q^20 + 354 * q^22 - 60 * q^25 + 16 * q^26 + 234 * q^28 + 638 * q^32 - 10 * q^34 + 472 * q^35 - 1884 * q^38 + 1764 * q^40 + 12 * q^41 - 880 * q^43 - 1320 * q^44 - 6 * q^46 + 4866 * q^50 - 3972 * q^52 + 6 * q^56 - 1640 * q^58 + 20 * q^59 - 5612 * q^62 + 4820 * q^64 - 508 * q^65 + 1832 * q^67 - 258 * q^68 + 1874 * q^70 + 724 * q^73 - 272 * q^76 - 554 * q^80 - 6534 * q^82 - 2664 * q^83 + 6 * q^86 - 914 * q^88 - 1080 * q^89 - 12 * q^91 - 3358 * q^92 - 5530 * q^94 + 5028 * q^97 - 9888 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1800, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)