Space of modular forms of level 1620, weight 2, and Character 1620.h

• Label: 1620.2.h
• Level: $1620$
• Weight: $2$
• Character orbit: 1620.h
• Rep. character: $\chi_{1620}(1619,\cdot)$
• Character field: $\Q$
• Dimension: $136$
• Sturm bound: $648$

Defining parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Sturm bound:			\(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1620, [\chi])\).

	Total	New	Old
Modular forms	348	152	196
Cusp forms	300	136	164
Eisenstein series	48	16	32

Trace form

\( 136 q + 4 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)