Space of modular forms of level 619, weight 2, and Character 619.g

• Label: 619.2.g
• Level: $619$
• Weight: $2$
• Character orbit: 619.g
• Rep. character: $\chi_{619}(4,\cdot)$
• Character field: $\Q(\zeta_{309})$
• Dimension: $10404$
• Newform subspaces: $1$
• Sturm bound: $103$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.g (of order \(309\) and degree \(204\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 619 \)
Character field:			\(\Q(\zeta_{309})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(103\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(619, [\chi])\).

	Total	New	Old
Modular forms	10812	10812	0
Cusp forms	10404	10404	0
Eisenstein series	408	408	0

Trace form

\( 10404 q - 206 q^{2} - 198 q^{3} - 158 q^{4} - 203 q^{5} - 209 q^{6} - 205 q^{7} - 200 q^{8} - 292 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(619, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
619.2.g.a	$619$	$2$	619.g	619.g	$309$	$10404$	$51$	$4.943$		None		$2$	$0$	\(-206\)	\(-198\)	\(-203\)	\(-205\)		$\mathrm{SU}(2)[C_{309}]$