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

• Label: 1584.4.cw
• Level: $1584$
• Weight: $4$
• Character orbit: 1584.cw
• Rep. character: $\chi_{1584}(497,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $1712$
• Sturm bound: $1152$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1584.cw (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(1152\)

Dimensions

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

	Total	New	Old
Modular forms	7008	1744	5264
Cusp forms	6816	1712	5104
Eisenstein series	192	32	160

Trace form

1712 * q + 6 * q^3 - 9 * q^5 + 5 * q^7 - 26 * q^9 + 12 * q^11 - 5 * q^13 - 42 * q^15 + 20 * q^19 + 24 * q^23 - 5153 * q^25 - 438 * q^27 - 15 * q^29 + 3 * q^31 + 439 * q^33 - 12 * q^37 - 2750 * q^39 - 15 * q^41 + 234 * q^45 - 1737 * q^47 - 9901 * q^49 - 770 * q^51 - 234 * q^55 - 2790 * q^57 + 9 * q^59 - 5 * q^61 + 10 * q^63 + 8 * q^67 - 2167 * q^69 - 20 * q^73 + 896 * q^75 - 996 * q^77 + 5 * q^79 - 466 * q^81 + 15 * q^83 - 5 * q^85 - 1360 * q^91 - 172 * q^93 + 15 * q^95 - 57 * q^97 - 5193 * q^99

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

\( S_{4}^{\mathrm{old}}(1584, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)