Space of modular forms of level 585, weight 4, and Character 585.cs

• Label: 585.4.cs
• Level: $585$
• Weight: $4$
• Character orbit: 585.cs
• Rep. character: $\chi_{585}(38,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $992$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	585.cs (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 585 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(585, [\chi])\).

	Total	New	Old
Modular forms	1024	1024	0
Cusp forms	992	992	0
Eisenstein series	32	32	0

Trace form

992 * q - 8 * q^3 - 16 * q^10 - 84 * q^12 - 2 * q^13 + 7544 * q^16 + 60 * q^22 - 636 * q^23 - 4 * q^25 - 284 * q^27 + 828 * q^30 + 80 * q^36 + 36 * q^38 + 252 * q^40 - 996 * q^42 - 4 * q^43 - 4360 * q^48 - 1312 * q^51 - 274 * q^52 + 984 * q^55 - 24 * q^56 - 8 * q^61 + 2082 * q^65 - 3888 * q^66 - 780 * q^68 + 3160 * q^75 + 3252 * q^77 + 5010 * q^78 + 5264 * q^81 + 7536 * q^82 - 2756 * q^87 - 444 * q^88 + 3832 * q^90 - 1024 * q^91 + 7572 * q^92 - 1512 * q^95

Decomposition of \(S_{4}^{\mathrm{new}}(585, [\chi])\) into newform subspaces

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