Space of modular forms of level 245, weight 2, and Character 245.x

• Label: 245.2.x
• Level: $245$
• Weight: $2$
• Character orbit: 245.x
• Rep. character: $\chi_{245}(3,\cdot)$
• Character field: $\Q(\zeta_{84})$
• Dimension: $624$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.x (of order \(84\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 245 \)
Character field:			\(\Q(\zeta_{84})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(245, [\chi])\).

	Total	New	Old
Modular forms	720	720	0
Cusp forms	624	624	0
Eisenstein series	96	96	0

Trace form

\( 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(245, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
245.2.x.a	$245$	$2$	245.x	245.x	$84$	$624$	$26$	$1.956$		None		$4$	$0$	\(-26\)	\(-22\)	\(-28\)	\(-18\)		$\mathrm{SU}(2)[C_{84}]$