Space of modular forms of level 3900, weight 2, and Character 3900.bs

• Label: 3900.2.bs
• Level: $3900$
• Weight: $2$
• Character orbit: 3900.bs
• Rep. character: $\chi_{3900}(1199,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $992$
• Sturm bound: $1680$

Defining parameters

Level:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3900.bs (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 780 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(1680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3900, [\chi])\).

	Total	New	Old
Modular forms	1728	1024	704
Cusp forms	1632	992	640
Eisenstein series	96	32	64

Trace form

\( 992 q + 4 q^{4} + 6 q^{6} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)