Space of modular forms of level 245, weight 4, and Character 245.s

• Label: 245.4.s
• Level: $245$
• Weight: $4$
• Character orbit: 245.s
• Rep. character: $\chi_{245}(13,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $984$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.s (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 245 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(245, [\chi])\).

	Total	New	Old
Modular forms	1032	1032	0
Cusp forms	984	984	0
Eisenstein series	48	48	0

Trace form

\( 984 q - 10 q^{2} - 14 q^{3} - 14 q^{5} + 28 q^{6} - 4 q^{7} - 126 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(245, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
245.4.s.a	$245$	$4$	245.s	245.s	$28$	$984$	$82$	$14.455$		None		$4$	$0$	\(-10\)	\(-14\)	\(-14\)	\(-4\)		$\mathrm{SU}(2)[C_{28}]$