Space of modular forms of level 1620, weight 4, and Character 1620.n

• Label: 1620.4.n
• Level: $1620$
• Weight: $4$
• Character orbit: 1620.n
• Rep. character: $\chi_{1620}(539,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $856$
• Sturm bound: $1296$

Defining parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1620.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 180 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1620, [\chi])\).

	Total	New	Old
Modular forms	1992	872	1120
Cusp forms	1896	856	1040
Eisenstein series	96	16	80

Trace form

\( 856 q + 4 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)