Space of modular forms of level 690, weight 2, and Character 690.n

• Label: 690.2.n
• Level: $690$
• Weight: $2$
• Character orbit: 690.n
• Rep. character: $\chi_{690}(89,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $480$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.n (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 345 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(690, [\chi])\).

	Total	New	Old
Modular forms	1520	480	1040
Cusp forms	1360	480	880
Eisenstein series	160	0	160

Trace form

\( 480 q - 48 q^{4} + 4 q^{6} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(690, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
690.2.n.a	$690$	$2$	690.n	345.n	$22$	$240$	$24$	$5.510$		None		$4$	$0$	\(-24\)	\(2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$
690.2.n.b	$690$	$2$	690.n	345.n	$22$	$240$	$24$	$5.510$		None		$4$	$0$	\(24\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{2}^{\mathrm{old}}(690, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)