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

• Label: 1568.2.b
• Level: $1568$
• Weight: $2$
• Character orbit: 1568.b
• Rep. character: $\chi_{1568}(785,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $7$
• Sturm bound: $448$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(448\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	256	46	210
Cusp forms	192	36	156
Eisenstein series	64	10	54

Trace form

\( 36 q - 24 q^{9} + O(q^{10}) \)

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.b.a	$1568$	$2$	1568.b	8.b	$2$	$2$	$2$	$12.521$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+3\beta q^{13}+\cdots\)
1568.2.b.b	$1568$	$2$	1568.b	8.b	$2$	$2$	$2$	$12.521$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{9}-\beta q^{11}-8q^{23}+5q^{25}-2\beta q^{29}+\cdots\)
1568.2.b.c	$1568$	$2$	1568.b	8.b	$2$	$4$	$4$	$12.521$	4.0.7168.1	\(\Q(\sqrt{-14}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-3+\beta _{3})q^{9}+(-2\beta _{1}+\cdots)q^{13}+\cdots\)
1568.2.b.d	$1568$	$2$	1568.b	8.b	$2$	$4$	$4$	$12.521$	4.0.2312.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-2+\beta _{3})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1568.2.b.e	$1568$	$2$	1568.b	8.b	$2$	$6$	$6$	$12.521$	6.0.1142512.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{2}+\beta _{5})q^{9}+\cdots\)
1568.2.b.f	$1568$	$2$	1568.b	8.b	$2$	$6$	$6$	$12.521$	6.0.1142512.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{2}+\beta _{5})q^{9}+\cdots\)
1568.2.b.g	$1568$	$2$	1568.b	8.b	$2$	$12$	$12$	$12.521$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}+\beta _{11}q^{5}+(-1-\beta _{4})q^{9}+\cdots\)

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

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