Space of modular forms of level 345, weight 2, and Character 345.s

• Label: 345.2.s
• Level: $345$
• Weight: $2$
• Character orbit: 345.s
• Rep. character: $\chi_{345}(11,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $320$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.s (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(345, [\chi])\).

	Total	New	Old
Modular forms	520	320	200
Cusp forms	440	320	120
Eisenstein series	80	0	80

Trace form

\( 320 q + 28 q^{4} - 2 q^{6} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(345, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
345.2.s.a	$345$	$2$	345.s	69.g	$22$	$160$	$16$	$2.755$		None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$
345.2.s.b	$345$	$2$	345.s	69.g	$22$	$160$	$16$	$2.755$		None		$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{2}^{\mathrm{old}}(345, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(345, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)