Space of modular forms of level 1380, weight 2, and Character 1380.n

• Label: 1380.2.n
• Level: $1380$
• Weight: $2$
• Character orbit: 1380.n
• Rep. character: $\chi_{1380}(689,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $576$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 345 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(576\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).

	Total	New	Old
Modular forms	300	48	252
Cusp forms	276	48	228
Eisenstein series	24	0	24

Trace form

\( 48 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1380, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1380.2.n.a	$1380$	$2$	1380.n	345.h	$2$	$48$	$48$	$11.019$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \)