Space of modular forms of level 3420, weight 2, and Character 3420.fh

• Label: 3420.2.fh
• Level: $3420$
• Weight: $2$
• Character orbit: 3420.fh
• Rep. character: $\chi_{3420}(359,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $1440$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3420.fh (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1140 \)
Character field:			\(\Q(\zeta_{18})\)
Sturm bound:			\(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3420, [\chi])\).

	Total	New	Old
Modular forms	4416	1440	2976
Cusp forms	4224	1440	2784
Eisenstein series	192	0	192

Trace form

\( 1440 q - 12 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3420, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3420, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3420, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 2}\)