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

• Label: 2790.2.h
• Level: $2790$
• Weight: $2$
• Character orbit: 2790.h
• Rep. character: $\chi_{2790}(2231,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $1152$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 93 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1152\)
Trace bound:			\(10\)

Dimensions

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

	Total	New	Old
Modular forms	592	48	544
Cusp forms	560	48	512
Eisenstein series	32	0	32

Trace form

\( 48 q - 48 q^{4} + 16 q^{7} + O(q^{10}) \)

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.h.a	$2790$	$2$	2790.h	93.c	$2$	$24$	$24$	$22.278$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$
2790.2.h.b	$2790$	$2$	2790.h	93.c	$2$	$24$	$24$	$22.278$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(558, [\chi])\)\(^{\oplus 2}\)