Space of modular forms of level 3600, weight 3, and Character 3600.be

• Label: 3600.3.be
• Level: $3600$
• Weight: $3$
• Character orbit: 3600.be
• Rep. character: $\chi_{3600}(1907,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $576$
• Sturm bound: $2160$

Defining parameters

Level:	\( N \)	\(=\)	\( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	3600.be (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 240 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(2160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3600, [\chi])\).

	Total	New	Old
Modular forms	2928	576	2352
Cusp forms	2832	576	2256
Eisenstein series	96	0	96

Trace form

\( 576 q + 16 q^{4} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)