Space of modular forms of level 400, weight 4, and Character 400.bl

• Label: 400.4.bl
• Level: $400$
• Weight: $4$
• Character orbit: 400.bl
• Rep. character: $\chi_{400}(29,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1424$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	400.bl (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 400 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(400, [\chi])\).

	Total	New	Old
Modular forms	1456	1456	0
Cusp forms	1424	1424	0
Eisenstein series	32	32	0

Trace form

\( 1424 q - 10 q^{2} - 10 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 200 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

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