Space of modular forms of level 309, weight 2, and Character 309.c

• Label: 309.2.c
• Level: $309$
• Weight: $2$
• Character orbit: 309.c
• Rep. character: $\chi_{309}(308,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $69$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	309.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 309 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(69\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(309, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	32	32	0
Eisenstein series	4	4	0

Trace form

\( 32 q - 32 q^{4} - 16 q^{7} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(309, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
309.2.c.a	$309$	$2$	309.c	309.c	$2$	$32$	$32$	$2.467$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{2}]$