Space of modular forms of level 600, weight 3, and Character 600.z

• Label: 600.3.z
• Level: $600$
• Weight: $3$
• Character orbit: 600.z
• Rep. character: $\chi_{600}(29,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $944$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	600.z (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 600 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(600, [\chi])\).

	Total	New	Old
Modular forms	976	976	0
Cusp forms	944	944	0
Eisenstein series	32	32	0

Trace form

\( 944 q - 6 q^{4} - 11 q^{6} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

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