Space of modular forms of level 900, weight 4, and Character 900.o

• Label: 900.4.o
• Level: $900$
• Weight: $4$
• Character orbit: 900.o
• Rep. character: $\chi_{900}(299,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $640$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	900.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 180 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(900, [\chi])\).

	Total	New	Old
Modular forms	1104	656	448
Cusp forms	1056	640	416
Eisenstein series	48	16	32

Trace form

\( 640 q + 2 q^{4} + 12 q^{6} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)