Space of modular forms of level 3920, weight 2, and Character 3920.k

• Label: 3920.2.k
• Level: $3920$
• Weight: $2$
• Character orbit: 3920.k
• Rep. character: $\chi_{3920}(2351,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $1344$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3920.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1344\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3920, [\chi])\).

	Total	New	Old
Modular forms	720	80	640
Cusp forms	624	80	544
Eisenstein series	96	0	96

Trace form

\( 80 q + 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3920, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3920.2.k.a	$3920$	$2$	3920.k	28.d	$2$	$8$	$8$	$31.301$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{16}^{5}+\zeta_{16}^{6})q^{3}+\zeta_{16}q^{5}+\cdots\)
3920.2.k.b	$3920$	$2$	3920.k	28.d	$2$	$8$	$8$	$31.301$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{5}q^{3}+\zeta_{24}q^{5}+(-1-\zeta_{24}^{3}+\cdots)q^{9}+\cdots\)
3920.2.k.c	$3920$	$2$	3920.k	28.d	$2$	$8$	$8$	$31.301$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\zeta_{16}^{5}-\zeta_{16}^{6})q^{3}+\zeta_{16}q^{5}+\cdots\)
3920.2.k.d	$3920$	$2$	3920.k	28.d	$2$	$12$	$12$	$31.301$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(2+\beta _{2}+\beta _{4})q^{9}+\cdots\)
3920.2.k.e	$3920$	$2$	3920.k	28.d	$2$	$12$	$12$	$31.301$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{6}q^{5}+(2+\beta _{2}+\beta _{4})q^{9}+\cdots\)
3920.2.k.f	$3920$	$2$	3920.k	28.d	$2$	$32$	$32$	$31.301$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \)