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

• Label: 245.2.p
• Level: $245$
• Weight: $2$
• Character orbit: 245.p
• Rep. character: $\chi_{245}(29,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $156$
• Newform subspaces: $2$
• Sturm bound: $56$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.p (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 245 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	180	180	0
Cusp forms	156	156	0
Eisenstein series	24	24	0

Trace form

\( 156 q + 14 q^{4} - 3 q^{5} - 32 q^{6} + 22 q^{9} + O(q^{10}) \)

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.p.a	$245$	$2$	245.p	245.p	$14$	$12$	$2$	$1.956$	\(\Q(\zeta_{28})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q-\zeta_{28}^{9}q^{2}+(-2\zeta_{28}^{3}+\zeta_{28}^{5}-\zeta_{28}^{7}+\cdots)q^{3}+\cdots\)
245.2.p.b	$245$	$2$	245.p	245.p	$14$	$144$	$24$	$1.956$		None		$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$