Space of modular forms of level 1568, weight 1, and Character 1568.d

• Label: 1568.1.d
• Level: $1568$
• Weight: $1$
• Character orbit: 1568.d
• Rep. character: $\chi_{1568}(1471,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1568.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1568, [\chi])\).

	Total	New	Old
Modular forms	44	4	40
Cusp forms	12	4	8
Eisenstein series	32	0	32

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	4	0	0

Trace form

\( 4 q - 4 q^{37} - 4 q^{53} - 4 q^{57} - 4 q^{81} + 4 q^{85} + 4 q^{93}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1568, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1568.1.d.a	$1568$	$1$	1568.d	4.b	$2$	$2$	$2$	$0.783$	\(\Q(\sqrt{-1}) \)	$A_{4}$	None	None					224.1.r.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-i q^{3}-q^{5}-i q^{11}+i q^{15}-q^{17}+\cdots\)
1568.1.d.b	$1568$	$1$	1568.d	4.b	$2$	$2$	$2$	$0.783$	\(\Q(\sqrt{-1}) \)	$A_{4}$	None	None					224.1.r.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-i q^{3}+q^{5}+i q^{11}-i q^{15}+q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1568, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)