Space of modular forms of level 105, weight 4, and Character 105.q

• Label: 105.4.q
• Level: $105$
• Weight: $4$
• Character orbit: 105.q
• Rep. character: $\chi_{105}(4,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(105, [\chi])\).

	Total	New	Old
Modular forms	104	48	56
Cusp forms	88	48	40
Eisenstein series	16	0	16

Trace form

\( 48 q + 96 q^{4} - 8 q^{5} + 48 q^{6} + 216 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(105, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.4.q.a	$105$	$4$	105.q	35.j	$6$	$4$	$2$	$6.195$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+5\zeta_{12}q^{2}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{3}+\cdots\)
105.4.q.b	$105$	$4$	105.q	35.j	$6$	$44$	$22$	$6.195$		None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)