Space of modular forms of level 448, weight 6, and Character 448.j

• Label: 448.6.j
• Level: $448$
• Weight: $6$
• Character orbit: 448.j
• Rep. character: $\chi_{448}(111,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $156$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	448.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(448, [\chi])\).

	Total	New	Old
Modular forms	656	164	492
Cusp forms	624	156	468
Eisenstein series	32	8	24

Trace form

\( 156 q + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(448, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(448, [\chi]) \cong \)