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

• Label: 245.2.f
• Level: $245$
• Weight: $2$
• Character orbit: 245.f
• Rep. character: $\chi_{245}(48,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $56$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(56\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	72	48	24
Cusp forms	40	32	8
Eisenstein series	32	16	16

Trace form

\( 32 q + 4 q^{2} - 4 q^{8} + O(q^{10}) \)

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.f.a	$245$	$2$	245.f	35.f	$4$	$4$	$2$	$1.956$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(-2\)	\(8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\)
245.2.f.b	$245$	$2$	245.f	35.f	$4$	$4$	$2$	$1.956$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(2\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
245.2.f.c	$245$	$2$	245.f	35.f	$4$	$24$	$12$	$1.956$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(245, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)