Space of modular forms of level 672, weight 4, and Character 672.bo

• Label: 672.4.bo
• Level: $672$
• Weight: $4$
• Character orbit: 672.bo
• Rep. character: $\chi_{672}(125,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $1520$
• Sturm bound: $512$

Defining parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.bo (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 672 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(672, [\chi])\).

	Total	New	Old
Modular forms	1552	1552	0
Cusp forms	1520	1520	0
Eisenstein series	32	32	0

Trace form

\( 1520 q - 16 q^{4} - 8 q^{7} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(672, [\chi])\) into newform subspaces

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