Space of modular forms of level 585, weight 6, and Character 585.cs

• Label: 585.6.cs
• Level: $585$
• Weight: $6$
• Character orbit: 585.cs
• Rep. character: $\chi_{585}(38,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1664$
• Sturm bound: $504$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	585.cs (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 585 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(585, [\chi])\).

	Total	New	Old
Modular forms	1696	1696	0
Cusp forms	1664	1664	0
Eisenstein series	32	32	0

Trace form

1664 * q - 8 * q^3 - 16 * q^10 - 852 * q^12 - 2 * q^13 + 206840 * q^16 + 252 * q^22 + 31620 * q^23 - 4 * q^25 + 5044 * q^27 + 19308 * q^30 + 14672 * q^36 + 97812 * q^38 + 4092 * q^40 - 3564 * q^42 - 4 * q^43 + 46904 * q^48 + 136424 * q^51 - 4162 * q^52 + 24984 * q^55 - 24 * q^56 - 8 * q^61 + 107922 * q^65 + 39792 * q^66 - 12300 * q^68 + 51340 * q^75 - 188700 * q^77 - 375870 * q^78 + 379184 * q^81 - 552336 * q^82 + 70336 * q^87 - 318684 * q^88 + 418192 * q^90 - 64696 * q^91 - 1517964 * q^92 - 37512 * q^95

Decomposition of \(S_{6}^{\mathrm{new}}(585, [\chi])\) into newform subspaces

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