Space of modular forms of level 390, weight 2, and Character 390.n

• Label: 390.2.n
• Level: $390$
• Weight: $2$
• Character orbit: 390.n
• Rep. character: $\chi_{390}(239,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 195 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(390, [\chi])\).

	Total	New	Old
Modular forms	184	56	128
Cusp forms	152	56	96
Eisenstein series	32	0	32

Trace form

\( 56 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(390, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
390.2.n.a	$390$	$2$	390.n	195.n	$4$	$56$	$28$	$3.114$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(390, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(390, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)