Space of modular forms of level 3640, weight 2, and Character 3640.bt

• Label: 3640.2.bt
• Level: $3640$
• Weight: $2$
• Character orbit: 3640.bt
• Rep. character: $\chi_{3640}(1273,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $336$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3640.bt (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 455 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3640, [\chi])\).

	Total	New	Old
Modular forms	1376	336	1040
Cusp forms	1312	336	976
Eisenstein series	64	0	64

Trace form

\( 336 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3640, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \)