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 - 6 * q^11 + 4 * q^14 + 2 * q^16 - 10 * q^19 + 4 * q^21 + 2 * q^24 + 8 * q^26 + 4 * q^31 - 6 * q^34 - 4 * q^36 + 8 * q^39 - 6 * q^41 + 6 * q^44 - 12 * q^46 + 6 * q^49 - 6 * q^51 - 10 * q^54 - 4 * q^56 + 4 * q^61 - 2 * q^64 + 6 * q^66 - 12 * q^69 + 24 * q^71 + 4 * q^74 + 10 * q^76 + 20 * q^79 + 2 * q^81 - 4 * q^84 + 8 * q^86 - 30 * q^89 - 16 * q^91 + 24 * q^94 - 2 * q^96 - 12 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓	✓	✓	50.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}-2 i q^{7}+\cdots\)