Space of modular forms of level 2790, weight 2, and Character 2790.e

• Label: 2790.2.e
• Level: $2790$
• Weight: $2$
• Character orbit: 2790.e
• Rep. character: $\chi_{2790}(2789,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $1152$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 465 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1152\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2790, [\chi])\).

	Total	New	Old
Modular forms	592	64	528
Cusp forms	560	64	496
Eisenstein series	32	0	32

Trace form

\( 64 q + 64 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2790, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2790.2.e.a	$2790$	$2$	2790.e	465.g	$2$	$32$	$32$	$22.278$		None		$4$	$0$	\(-32\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
2790.2.e.b	$2790$	$2$	2790.e	465.g	$2$	$32$	$32$	$22.278$		None		$4$	$0$	\(32\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2790, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1395, [\chi])\)\(^{\oplus 2}\)