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

• Label: 619.2.e
• Level: $619$
• Weight: $2$
• Character orbit: 619.e
• Rep. character: $\chi_{619}(9,\cdot)$
• Character field: $\Q(\zeta_{103})$
• Dimension: $5100$
• Newform subspaces: $1$
• Sturm bound: $103$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.e (of order \(103\) and degree \(102\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 619 \)
Character field:			\(\Q(\zeta_{103})\)
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	5304	5304	0
Cusp forms	5100	5100	0
Eisenstein series	204	204	0

Trace form

\( 5100 q - 100 q^{2} - 95 q^{3} - 144 q^{4} - 97 q^{5} - 91 q^{6} - 93 q^{7} - 94 q^{8} - 139 q^{9} + O(q^{10}) \)

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.e.a	$619$	$2$	619.e	619.e	$103$	$5100$	$50$	$4.943$		None		$2$	$0$	\(-100\)	\(-95\)	\(-97\)	\(-93\)		$\mathrm{SU}(2)[C_{103}]$