Space of modular forms of level 102, weight 2, and Character 102.b

• Label: 102.2.b
• Level: $102$
• Weight: $2$
• Character orbit: 102.b
• Rep. character: $\chi_{102}(67,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	102.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(102, [\chi])\).

	Total	New	Old
Modular forms	22	2	20
Cusp forms	14	2	12
Eisenstein series	8	0	8

Trace form

\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(102, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
102.2.b.a	$102$	$2$	102.b	17.b	$2$	$2$	$2$	$0.814$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+iq^{3}+q^{4}-2iq^{5}+iq^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(102, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(102, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)