Space of modular forms of level 1568, weight 2, and Character 1568.f

• Label: 1568.2.f
• Level: $1568$
• Weight: $2$
• Character orbit: 1568.f
• Rep. character: $\chi_{1568}(1567,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $448$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(448\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1568, [\chi])\).

	Total	New	Old
Modular forms	256	40	216
Cusp forms	192	40	152
Eisenstein series	64	0	64

Trace form

\( 40 q + 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1568, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1568.2.f.a	$1568$	$2$	1568.f	28.d	$2$	$8$	$8$	$12.521$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{16}^{7}q^{3}+(-\zeta_{16}^{2}+\zeta_{16}^{4})q^{5}+\cdots\)
1568.2.f.b	$1568$	$2$	1568.f	28.d	$2$	$16$	$16$	$12.521$	16.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{13}q^{5}+(1-\beta _{2})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots\)
1568.2.f.c	$1568$	$2$	1568.f	28.d	$2$	$16$	$16$	$12.521$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{12}q^{3}+(\beta _{5}+\beta _{7})q^{5}+(2+\beta _{3})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1568, [\chi]) \cong \)