Space of modular forms of level 400, weight 6, and Character 400.j

• Label: 400.6.j
• Level: $400$
• Weight: $6$
• Character orbit: 400.j
• Rep. character: $\chi_{400}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $356$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	400.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(400, [\chi])\).

	Total	New	Old
Modular forms	612	364	248
Cusp forms	588	356	232
Eisenstein series	24	8	16

Trace form

\( 356 q + 2 q^{2} + 40 q^{4} - 4 q^{6} + 4 q^{7} + 248 q^{8} - 28188 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(400, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)