Space of modular forms of level 603, weight 2, and Character 603.e

• Label: 603.2.e
• Level: $603$
• Weight: $2$
• Character orbit: 603.e
• Rep. character: $\chi_{603}(202,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $132$
• Newform subspaces: $2$
• Sturm bound: $136$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(136\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(603, [\chi])\).

	Total	New	Old
Modular forms	140	132	8
Cusp forms	132	132	0
Eisenstein series	8	0	8

Trace form

\( 132 q - 66 q^{4} - 6 q^{6} - 12 q^{8} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(603, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
603.2.e.a	$603$	$2$	603.e	9.c	$3$	$66$	$33$	$4.815$		None		✓			603.2.e.a	$2$	$0$	\(-7\)	\(0\)	\(-18\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$
603.2.e.b	$603$	$2$	603.e	9.c	$3$	$66$	$33$	$4.815$		None		✓			603.2.e.b	$2$	$0$	\(7\)	\(0\)	\(18\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$