Space of modular forms of level 50, weight 2, and Character 50.b

• Label: 50.2.b
• Level: $50$
• Weight: $2$
• Character orbit: 50.b
• Rep. character: $\chi_{50}(49,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(50, [\chi])\).

	Total	New	Old
Modular forms	14	2	12
Cusp forms	2	2	0
Eisenstein series	12	0	12

Trace form

\( 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(50, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
50.2.b.a	$50$	$2$	50.b	5.b	$2$	$2$	$2$	$0.399$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}-2iq^{7}+\cdots\)