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

• Label: 3420.2.m
• Level: $3420$
• Weight: $2$
• Character orbit: 3420.m
• Rep. character: $\chi_{3420}(379,\cdot)$
• Character field: $\Q$
• Dimension: $296$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3420.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 380 \)
Character field:			\(\Q\)
Sturm bound:			\(1440\)

Dimensions

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

	Total	New	Old
Modular forms	736	304	432
Cusp forms	704	296	408
Eisenstein series	32	8	24

Trace form

\( 296 q - 8 q^{4} + 4 q^{5} + O(q^{10}) \)

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

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