Space of modular forms of level 1056, weight 2, and Character 1056.y

• Label: 1056.2.y
• Level: $1056$
• Weight: $2$
• Character orbit: 1056.y
• Rep. character: $\chi_{1056}(97,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $96$
• Newform subspaces: $10$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1056 = 2^{5} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1056.y (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1056, [\chi])\).

	Total	New	Old
Modular forms	832	96	736
Cusp forms	704	96	608
Eisenstein series	128	0	128

Trace form

\( 96 q - 24 q^{9} - 40 q^{25} - 8 q^{33} + 48 q^{41} + 8 q^{49} - 32 q^{53} - 32 q^{61} - 32 q^{65} + 24 q^{73} + 112 q^{77} - 24 q^{81} + 144 q^{85} + 32 q^{89} + 48 q^{93} + 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1056, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1056.2.y.a	$1056$	$2$	1056.y	11.c	$5$	$4$	$1$	$8.432$	\(\Q(\zeta_{10})\)	None		✓			1056.2.y.a	$2$	$1$	\(0\)	\(-1\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}-\zeta_{10}^{2})q^{5}+\cdots\)
1056.2.y.b	$1056$	$2$	1056.y	11.c	$5$	$4$	$1$	$8.432$	\(\Q(\zeta_{10})\)	None		✓			1056.2.y.a	$2$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}-\zeta_{10}^{2})q^{5}+\cdots\)
1056.2.y.c	$1056$	$2$	1056.y	11.c	$5$	$8$	$2$	$8.432$	8.0.484000000.9	None		✓			1056.2.y.c	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{3}q^{3}+(-\beta _{2}-\beta _{6})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
1056.2.y.d	$1056$	$2$	1056.y	11.c	$5$	$8$	$2$	$8.432$	8.0.484000000.9	None		✓			1056.2.y.c	$2$	$0$	\(0\)	\(2\)	\(2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{3}q^{3}+(-\beta _{2}-\beta _{6})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
1056.2.y.e	$1056$	$2$	1056.y	11.c	$5$	$12$	$3$	$8.432$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1056.2.y.e	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{7}q^{3}+(1-\beta _{5}-\beta _{7}-\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots\)
1056.2.y.f	$1056$	$2$	1056.y	11.c	$5$	$12$	$3$	$8.432$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1056.2.y.f	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{6}q^{3}+(-\beta _{5}+\beta _{8}+\beta _{11})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1056.2.y.g	$1056$	$2$	1056.y	11.c	$5$	$12$	$3$	$8.432$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1056.2.y.g	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{5}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3}+2\beta _{4}+\cdots)q^{5}+\cdots\)
1056.2.y.h	$1056$	$2$	1056.y	11.c	$5$	$12$	$3$	$8.432$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1056.2.y.g	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{5}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3}+2\beta _{4}+\cdots)q^{5}+\cdots\)
1056.2.y.i	$1056$	$2$	1056.y	11.c	$5$	$12$	$3$	$8.432$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1056.2.y.f	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{6}q^{3}+(-\beta _{5}+\beta _{8}+\beta _{11})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1056.2.y.j	$1056$	$2$	1056.y	11.c	$5$	$12$	$3$	$8.432$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1056.2.y.e	$2$	$0$	\(0\)	\(3\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{7}q^{3}+(1-\beta _{5}-\beta _{7}-\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1056, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1056, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)