Space of modular forms of level 1071, weight 2, and Character 1071.d

• Label: 1071.2.d
• Level: $1071$
• Weight: $2$
• Character orbit: 1071.d
• Rep. character: $\chi_{1071}(188,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1071, [\chi])\).

	Total	New	Old
Modular forms	152	40	112
Cusp forms	136	40	96
Eisenstein series	16	0	16

Trace form

\( 40 q - 32 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1071, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1071.2.d.a	$1071$	$2$	1071.d	21.c	$2$	$4$	$4$	$8.552$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		✓			1071.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots\)
1071.2.d.b	$1071$	$2$	1071.d	21.c	$2$	$4$	$4$	$8.552$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		✓			1071.2.d.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}+(1+\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
1071.2.d.c	$1071$	$2$	1071.d	21.c	$2$	$16$	$16$	$8.552$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			1071.2.d.c	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{14}q^{5}+\cdots\)
1071.2.d.d	$1071$	$2$	1071.d	21.c	$2$	$16$	$16$	$8.552$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			1071.2.d.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1071, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1071, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)