Newform orbit 960.4.a.r

• Label: 960.4.a.r
• Level: $960$
• Weight: $4$
• Character orbit: 960.a
• Self dual: yes
• Analytic conductor: $56.642$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$960 = 2^{6} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	960.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$56.6418336055$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 60)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 3 * q^3 + 5 * q^5 + 28 * q^7 + 9 * q^9 - 24 * q^11 + 70 * q^13 - 15 * q^15 + 102 * q^17 + 20 * q^19 - 84 * q^21 + 72 * q^23 + 25 * q^25 - 27 * q^27 - 306 * q^29 + 136 * q^31 + 72 * q^33 + 140 * q^35 + 214 * q^37 - 210 * q^39 - 150 * q^41 - 292 * q^43 + 45 * q^45 + 72 * q^47 + 441 * q^49 - 306 * q^51 + 414 * q^53 - 120 * q^55 - 60 * q^57 - 744 * q^59 + 418 * q^61 + 252 * q^63 + 350 * q^65 + 188 * q^67 - 216 * q^69 - 480 * q^71 + 434 * q^73 - 75 * q^75 - 672 * q^77 - 1352 * q^79 + 81 * q^81 - 612 * q^83 + 510 * q^85 + 918 * q^87 - 30 * q^89 + 1960 * q^91 - 408 * q^93 + 100 * q^95 - 286 * q^97 - 216 * q^99

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

Label  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1.1

0

0

−3.00000

0

5.00000

0

28.0000

0

9.00000

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$+1$
$5$	$-1$

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	960.4.a.r		1
4.b	odd	2	1		960.4.a.bc		1
8.b	even	2	1		240.4.a.i		1
8.d	odd	2	1		60.4.a.a	✓	1
24.f	even	2	1		180.4.a.d		1
24.h	odd	2	1		720.4.a.bb		1
40.e	odd	2	1		300.4.a.i		1
40.f	even	2	1		1200.4.a.a		1
40.i	odd	4	2		1200.4.f.n		2
40.k	even	4	2		300.4.d.b		2
72.l	even	6	2		1620.4.i.f		2
72.p	odd	6	2		1620.4.i.l		2
120.m	even	2	1		900.4.a.q		1
120.q	odd	4	2		900.4.d.h		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
60.4.a.a	✓	1	8.d	odd	2	1
180.4.a.d		1	24.f	even	2	1
240.4.a.i		1	8.b	even	2	1
300.4.a.i		1	40.e	odd	2	1
300.4.d.b		2	40.k	even	4	2
720.4.a.bb		1	24.h	odd	2	1
900.4.a.q		1	120.m	even	2	1
900.4.d.h		2	120.q	odd	4	2
960.4.a.r		1	1.a	even	1	1	trivial
960.4.a.bc		1	4.b	odd	2	1
1200.4.a.a		1	40.f	even	2	1
1200.4.f.n		2	40.i	odd	4	2
1620.4.i.f		2	72.l	even	6	2
1620.4.i.l		2	72.p	odd	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(960))$:

$T_{7} - 28$

$T_{11} + 24$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T + 3$
$5$	$T - 5$
$7$	$T - 28$
$11$	$T + 24$