Space of modular forms of level 196, weight 6, and Character 196.p

• Label: 196.6.p
• Level: $196$
• Weight: $6$
• Character orbit: 196.p
• Rep. character: $\chi_{196}(3,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1656$
• Sturm bound: $168$

Defining parameters

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.p (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 196 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(196, [\chi])\).

	Total	New	Old
Modular forms	1704	1704	0
Cusp forms	1656	1656	0
Eisenstein series	48	48	0

Trace form

\( 1656 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} + 236 q^{8} + 10828 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

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