Space of modular forms of level 588, weight 3, and Character 588.r

• Label: 588.3.r
• Level: $588$
• Weight: $3$
• Character orbit: 588.r
• Rep. character: $\chi_{588}(83,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $1320$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.r (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 588 \)
Character field:			\(\Q(\zeta_{14})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(588, [\chi])\).

	Total	New	Old
Modular forms	1368	1368	0
Cusp forms	1320	1320	0
Eisenstein series	48	48	0

Trace form

\( 1320 q - 10 q^{4} - 7 q^{6} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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