Space of modular forms of level 1456, weight 2, and Character 1456.r

• Label: 1456.2.r
• Level: $1456$
• Weight: $2$
• Character orbit: 1456.r
• Rep. character: $\chi_{1456}(417,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $18$
• Sturm bound: $448$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.r (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(448\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1456, [\chi])\).

	Total	New	Old
Modular forms	472	96	376
Cusp forms	424	96	328
Eisenstein series	48	0	48

Trace form

\( 96 q - 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1456, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1456.2.r.a	$1456$	$2$	1456.r	7.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					364.2.j.d	$2$	$0$	\(0\)	\(-3\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1456.2.r.b	$1456$	$2$	1456.r	7.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					364.2.j.c	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1456.2.r.c	$1456$	$2$	1456.r	7.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					728.2.r.a	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1456.2.r.d	$1456$	$2$	1456.r	7.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					728.2.r.b	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1456.2.r.e	$1456$	$2$	1456.r	7.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					728.2.r.c	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1456.2.r.f	$1456$	$2$	1456.r	7.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					182.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(1-\zeta_{6})q^{11}+\cdots\)
1456.2.r.g	$1456$	$2$	1456.r	7.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					91.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(-3+3\zeta_{6})q^{11}+\cdots\)
1456.2.r.h	$1456$	$2$	1456.r	7.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					364.2.j.a	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1456.2.r.i	$1456$	$2$	1456.r	7.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					364.2.j.b	$2$	$0$	\(0\)	\(1\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1456.2.r.j	$1456$	$2$	1456.r	7.c	$3$	$4$	$2$	$11.626$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					91.2.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(3+2\beta _{1})q^{7}+\cdots\)
1456.2.r.k	$1456$	$2$	1456.r	7.c	$3$	$4$	$2$	$11.626$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None					728.2.r.d	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+2\beta _{2})q^{3}+(\beta _{1}+\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
1456.2.r.l	$1456$	$2$	1456.r	7.c	$3$	$6$	$3$	$11.626$	6.0.309123.1	None					182.2.f.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{2}+\beta _{3}+\beta _{5})q^{3}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
1456.2.r.m	$1456$	$2$	1456.r	7.c	$3$	$8$	$4$	$11.626$	8.0.\(\cdots\).1	None					728.2.r.e	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
1456.2.r.n	$1456$	$2$	1456.r	7.c	$3$	$8$	$4$	$11.626$	8.0.8681953329.1	None					182.2.f.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-7\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{7})q^{3}+(-\beta _{2}+\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
1456.2.r.o	$1456$	$2$	1456.r	7.c	$3$	$8$	$4$	$11.626$	8.0.856615824.2	None					364.2.j.e	$2$	$0$	\(0\)	\(3\)	\(1\)	\(-1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2}-\beta _{6})q^{3}+(-\beta _{1}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
1456.2.r.p	$1456$	$2$	1456.r	7.c	$3$	$10$	$5$	$11.626$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					91.2.e.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{9}q^{3}+(-\beta _{3}-\beta _{7})q^{5}+(\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots\)
1456.2.r.q	$1456$	$2$	1456.r	7.c	$3$	$14$	$7$	$11.626$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					728.2.r.f	$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}-\beta _{9}q^{5}+\beta _{4}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
1456.2.r.r	$1456$	$2$	1456.r	7.c	$3$	$16$	$8$	$11.626$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		728.2.r.g	$2$	$0$	\(0\)	\(2\)	\(0\)	\(-1\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(\beta _{4}+\beta _{10})q^{5}+(\beta _{5}-\beta _{12}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)