Space of modular forms of level 105, weight 3, and Character 105.k

• Label: 105.3.k
• Level: $105$
• Weight: $3$
• Character orbit: 105.k
• Rep. character: $\chi_{105}(62,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(105, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	56	56	0
Eisenstein series	16	16	0

Trace form

\( 56 q + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(105, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.3.k.a	$105$	$3$	105.k	105.k	$4$	$4$	$2$	$2.861$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-28\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+(-2-\zeta_{8}+2\zeta_{8}^{2})q^{3}-3\zeta_{8}^{2}q^{4}+\cdots\)
105.3.k.b	$105$	$3$	105.k	105.k	$4$	$4$	$2$	$2.861$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+(2+\zeta_{8}-2\zeta_{8}^{2})q^{3}-3\zeta_{8}^{2}q^{4}+\cdots\)
105.3.k.c	$105$	$3$	105.k	105.k	$4$	$16$	$8$	$2.861$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(32\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+(\beta _{7}+\beta _{10}-\beta _{13}+\beta _{15})q^{3}+\cdots\)
105.3.k.d	$105$	$3$	105.k	105.k	$4$	$32$	$16$	$2.861$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$