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

• Label: 1456.2.s
• Level: $1456$
• Weight: $2$
• Character orbit: 1456.s
• Rep. character: $\chi_{1456}(113,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $84$
• Newform subspaces: $19$
• Sturm bound: $448$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.s (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(448\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	472	84	388
Cusp forms	424	84	340
Eisenstein series	48	0	48

Trace form

84 * q + 4 * q^5 - 42 * q^9 + 2 * q^13 + 2 * q^17 + 12 * q^23 + 80 * q^25 + 24 * q^27 - 2 * q^29 - 12 * q^35 - 10 * q^37 - 36 * q^39 + 2 * q^41 + 4 * q^43 - 10 * q^45 + 48 * q^47 - 42 * q^49 + 24 * q^51 + 4 * q^53 + 40 * q^55 + 16 * q^57 + 36 * q^59 - 10 * q^61 + 2 * q^65 + 24 * q^67 + 12 * q^71 - 20 * q^73 + 16 * q^75 - 64 * q^79 - 50 * q^81 + 40 * q^83 + 18 * q^85 + 12 * q^87 - 28 * q^89 - 48 * q^93 - 12 * q^97 - 152 * q^99

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.s.a	$1456$	$2$	1456.s	13.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					182.2.g.c	$2$	$0$	\(0\)	\(-2\)	\(-6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}-3q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1456.2.s.b	$1456$	$2$	1456.s	13.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					182.2.g.d	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1456.2.s.c	$1456$	$2$	1456.s	13.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					364.2.k.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{5}-\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-2+2\zeta_{6})q^{11}+\cdots\)
1456.2.s.d	$1456$	$2$	1456.s	13.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					364.2.k.b	$2$	$0$	\(0\)	\(0\)	\(6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3q^{5}+\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-2+2\zeta_{6})q^{11}+\cdots\)
1456.2.s.e	$1456$	$2$	1456.s	13.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					182.2.g.b	$2$	$0$	\(0\)	\(1\)	\(6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+3q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1456.2.s.f	$1456$	$2$	1456.s	13.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					728.2.s.a	$2$	$0$	\(0\)	\(2\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1456.2.s.g	$1456$	$2$	1456.s	13.c	$3$	$2$	$1$	$11.626$	\(\Q(\sqrt{-3}) \)	None					182.2.g.a	$2$	$0$	\(0\)	\(3\)	\(-6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{3}-3q^{5}+\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
1456.2.s.h	$1456$	$2$	1456.s	13.c	$3$	$4$	$2$	$11.626$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					91.2.f.a	$2$	$0$	\(0\)	\(-3\)	\(6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1}-\beta _{3})q^{3}+(1-\beta _{2})q^{5}+\cdots\)
1456.2.s.i	$1456$	$2$	1456.s	13.c	$3$	$4$	$2$	$11.626$	\(\Q(\zeta_{12})\)	None					728.2.s.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_{2}-\beta_1)q^{3}-\beta_{3} q^{5}+(\beta_1-1)q^{7}+\cdots\)
1456.2.s.j	$1456$	$2$	1456.s	13.c	$3$	$4$	$2$	$11.626$	\(\Q(\zeta_{12})\)	None					728.2.s.d	$2$	$0$	\(0\)	\(-2\)	\(8\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}+\cdots)q^{5}+\cdots\)
1456.2.s.k	$1456$	$2$	1456.s	13.c	$3$	$4$	$2$	$11.626$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None					364.2.k.d	$2$	$0$	\(0\)	\(-1\)	\(-6\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{3}+(-2+\beta _{2})q^{5}-\beta _{1}q^{7}+(2\beta _{1}+\cdots)q^{9}+\cdots\)
1456.2.s.l	$1456$	$2$	1456.s	13.c	$3$	$4$	$2$	$11.626$	\(\Q(\zeta_{12})\)	None					182.2.g.e	$2$	$0$	\(0\)	\(0\)	\(8\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_{2} q^{3}+(-\beta_{3}+2)q^{5}+(\beta_1-1)q^{7}+\cdots\)
1456.2.s.m	$1456$	$2$	1456.s	13.c	$3$	$4$	$2$	$11.626$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None					364.2.k.c	$2$	$0$	\(0\)	\(1\)	\(6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(1+\beta _{3})q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1456.2.s.n	$1456$	$2$	1456.s	13.c	$3$	$4$	$2$	$11.626$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					728.2.s.b	$2$	$0$	\(0\)	\(1\)	\(10\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+\beta _{3}q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
1456.2.s.o	$1456$	$2$	1456.s	13.c	$3$	$4$	$2$	$11.626$	\(\Q(\zeta_{12})\)	None					91.2.f.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_{2}+\beta_1)q^{3}-\beta_{3} q^{5}+(-\beta_1+1)q^{7}+\cdots\)
1456.2.s.p	$1456$	$2$	1456.s	13.c	$3$	$8$	$4$	$11.626$	8.0.\(\cdots\).1	None					728.2.s.f	$2$	$0$	\(0\)	\(-3\)	\(-10\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{4})q^{3}+(-1-\beta _{6})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots\)
1456.2.s.q	$1456$	$2$	1456.s	13.c	$3$	$8$	$4$	$11.626$	8.0.\(\cdots\).1	None					91.2.f.c	$2$	$0$	\(0\)	\(1\)	\(-14\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{5}+\beta _{6})q^{3}+(-2-\beta _{3})q^{5}+\beta _{4}q^{7}+\cdots\)
1456.2.s.r	$1456$	$2$	1456.s	13.c	$3$	$8$	$4$	$11.626$	8.0.4277552409.3	None					728.2.s.e	$2$	$0$	\(0\)	\(3\)	\(-10\)	\(4\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}+\beta _{7})q^{5}+\cdots\)
1456.2.s.s	$1456$	$2$	1456.s	13.c	$3$	$14$	$7$	$11.626$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None			✓		728.2.s.g	$2$	$0$	\(0\)	\(1\)	\(4\)	\(-7\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)