Space of modular forms of level 1620, weight 3, and Character 1620.bn

• Label: 1620.3.bn
• Level: $1620$
• Weight: $3$
• Character orbit: 1620.bn
• Rep. character: $\chi_{1620}(31,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $7776$
• Sturm bound: $972$

Defining parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1620.bn (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 324 \)
Character field:			\(\Q(\zeta_{54})\)
Sturm bound:			\(972\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1620, [\chi])\).

	Total	New	Old
Modular forms	11736	7776	3960
Cusp forms	11592	7776	3816
Eisenstein series	144	0	144

Trace form

\( 7776 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)