Space of modular forms of level 490, weight 6, and Character 490.t

• Label: 490.6.t
• Level: $490$
• Weight: $6$
• Character orbit: 490.t
• Rep. character: $\chi_{490}(9,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1680$
• Sturm bound: $504$

Defining parameters

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	490.t (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 245 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(490, [\chi])\).

	Total	New	Old
Modular forms	5088	1680	3408
Cusp forms	4992	1680	3312
Eisenstein series	96	0	96

Trace form

\( 1680 q - 2240 q^{4} - 22 q^{5} + 488 q^{6} - 12860 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(490, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(490, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(490, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)