Space of modular forms of level 105, weight 2, and Character 105.b

• Label: 105.2.b
• Level: $105$
• Weight: $2$
• Character orbit: 105.b
• Rep. character: $\chi_{105}(41,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $32$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(32\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

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

Trace form

\( 12 q - 16 q^{4} - 8 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.2.b.a	$105$	$2$	105.b	21.c	$2$	$2$	$2$	$0.838$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-q^{5}-3q^{6}+\cdots\)
105.2.b.b	$105$	$2$	105.b	21.c	$2$	$2$	$2$	$0.838$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+q^{5}+3q^{6}+\cdots\)
105.2.b.c	$105$	$2$	105.b	21.c	$2$	$4$	$4$	$0.838$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-1\)	\(-4\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots\)
105.2.b.d	$105$	$2$	105.b	21.c	$2$	$4$	$4$	$0.838$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(1\)	\(4\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots\)