Space of modular forms of level 630, weight 4, and Character 630.i

• Label: 630.4.i
• Level: $630$
• Weight: $4$
• Character orbit: 630.i
• Rep. character: $\chi_{630}(121,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $192$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(630, [\chi])\).

	Total	New	Old
Modular forms	880	192	688
Cusp forms	848	192	656
Eisenstein series	32	0	32

Trace form

\( 192 q + 768 q^{4} - 20 q^{5} - 8 q^{6} - 24 q^{7} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(630, [\chi]) \cong \)