Space of modular forms of level 3744, weight 2, and Character 3744.em

• Label: 3744.2.em
• Level: $3744$
• Weight: $2$
• Character orbit: 3744.em
• Rep. character: $\chi_{3744}(1061,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $896$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3744.em (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1248 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3744, [\chi])\).

	Total	New	Old
Modular forms	2720	896	1824
Cusp forms	2656	896	1760
Eisenstein series	64	0	64

Trace form

\( 896 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)