Space of modular forms of level 1584, weight 4, and Character 1584.ck

• Label: 1584.4.ck
• Level: $1584$
• Weight: $4$
• Character orbit: 1584.ck
• Rep. character: $\chi_{1584}(133,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $2880$
• Sturm bound: $1152$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1584.ck (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1584, [\chi])\).

	Total	New	Old
Modular forms	3472	2880	592
Cusp forms	3440	2880	560
Eisenstein series	32	0	32

Trace form

2880 * q - 60 * q^6 - 312 * q^12 + 140 * q^18 + 308 * q^20 + 1000 * q^24 + 264 * q^27 + 1692 * q^30 + 1960 * q^32 - 580 * q^36 - 2408 * q^38 + 3500 * q^42 - 144 * q^46 - 3760 * q^47 + 2464 * q^48 + 70560 * q^49 - 2132 * q^50 - 1400 * q^51 - 1000 * q^56 - 1188 * q^58 - 2040 * q^59 - 7932 * q^60 - 3912 * q^62 - 1080 * q^64 + 1100 * q^66 + 7952 * q^72 + 3640 * q^74 + 6608 * q^75 - 2232 * q^76 + 3320 * q^78 + 2808 * q^82 + 2440 * q^83 - 8968 * q^84 - 5560 * q^86 + 8788 * q^90 - 4272 * q^93 + 13228 * q^96 + 12104 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1584, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)