Space of modular forms of level 570, weight 6, and Character 570.n

• Label: 570.6.n
• Level: $570$
• Weight: $6$
• Character orbit: 570.n
• Rep. character: $\chi_{570}(179,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $400$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 285 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(570, [\chi])\).

	Total	New	Old
Modular forms	1216	400	816
Cusp forms	1184	400	784
Eisenstein series	32	0	32

Trace form

\( 400 q + 3200 q^{4} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(570, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(570, [\chi]) \cong \)