Space of modular forms of level 290, weight 2, and Character 290.b

• Label: 290.2.b
• Level: $290$
• Weight: $2$
• Character orbit: 290.b
• Rep. character: $\chi_{290}(59,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $90$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(90\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(290, [\chi])\).

	Total	New	Old
Modular forms	50	14	36
Cusp forms	42	14	28
Eisenstein series	8	0	8

Trace form

\( 14 q - 14 q^{4} - 22 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(290, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
290.2.b.a	$290$	$2$	290.b	5.b	$2$	$4$	$4$	$2.316$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(-\beta _{1}+\beta _{3})q^{3}-q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
290.2.b.b	$290$	$2$	290.b	5.b	$2$	$10$	$10$	$2.316$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{5})q^{3}-q^{4}+\beta _{3}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(290, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(290, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)