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

• Label: 105.4.u
• Level: $105$
• Weight: $4$
• Character orbit: 105.u
• Rep. character: $\chi_{105}(52,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.u (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	208	96	112
Cusp forms	176	96	80
Eisenstein series	32	0	32

Trace form

\( 96 q + 48 q^{5} - 4 q^{7} + 168 q^{8} + O(q^{10}) \)

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.u.a	$105$	$4$	105.u	35.k	$12$	$96$	$24$	$6.195$		None		$4$	$0$	\(0\)	\(0\)	\(48\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$

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

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