Space of modular forms of level 106, weight 2, and Character 106.b

• Label: 106.2.b
• Level: $106$
• Weight: $2$
• Character orbit: 106.b
• Rep. character: $\chi_{106}(105,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $27$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 106 = 2 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	106.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(27\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(106, [\chi])\).

	Total	New	Old
Modular forms	16	4	12
Cusp forms	12	4	8
Eisenstein series	4	0	4

Trace form

\( 4 q - 4 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(106, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
106.2.b.a	$106$	$2$	106.b	53.b	$2$	$2$	$2$	$0.846$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}+2iq^{5}-q^{6}+\cdots\)
106.2.b.b	$106$	$2$	106.b	53.b	$2$	$2$	$2$	$0.846$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2iq^{3}-q^{4}-iq^{5}+2q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(106, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(106, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 2}\)