Newform orbit 1600.4.a.m

• Label: 1600.4.a.m
• Level: $1600$
• Weight: $4$
• Character orbit: 1600.a
• Self dual: yes
• Analytic conductor: $94.403$
• Analytic rank: $2$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$1600 = 2^{6} \cdot 5^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1600.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$94.4030560092$
Analytic rank:	$2$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 200)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 5 * q^3 + 2 * q^7 - 2 * q^9 - 39 * q^11 - 84 * q^13 - 61 * q^17 - 151 * q^19 - 10 * q^21 - 58 * q^23 + 145 * q^27 - 192 * q^29 - 18 * q^31 + 195 * q^33 + 138 * q^37 + 420 * q^39 + 229 * q^41 + 164 * q^43 - 212 * q^47 - 339 * q^49 + 305 * q^51 - 578 * q^53 + 755 * q^57 + 336 * q^59 - 858 * q^61 - 4 * q^63 + 209 * q^67 + 290 * q^69 - 780 * q^71 - 403 * q^73 - 78 * q^77 - 230 * q^79 - 671 * q^81 + 1293 * q^83 + 960 * q^87 - 1369 * q^89 - 168 * q^91 + 90 * q^93 + 382 * q^97 + 78 * 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

−5.00000

0

0

0

2.00000

0

−2.00000

0

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$5$	$+1$

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	1600.4.a.m		1
4.b	odd	2	1		1600.4.a.bo		1
5.b	even	2	1		1600.4.a.bn		1
8.b	even	2	1		200.4.a.h	yes	1
8.d	odd	2	1		400.4.a.f		1
20.d	odd	2	1		1600.4.a.n		1
24.h	odd	2	1		1800.4.a.t		1
40.e	odd	2	1		400.4.a.q		1
40.f	even	2	1		200.4.a.c	✓	1
40.i	odd	4	2		200.4.c.d		2
40.k	even	4	2		400.4.c.g		2
120.i	odd	2	1		1800.4.a.p		1
120.w	even	4	2		1800.4.f.c		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
200.4.a.c	✓	1	40.f	even	2	1
200.4.a.h	yes	1	8.b	even	2	1
200.4.c.d		2	40.i	odd	4	2
400.4.a.f		1	8.d	odd	2	1
400.4.a.q		1	40.e	odd	2	1
400.4.c.g		2	40.k	even	4	2
1600.4.a.m		1	1.a	even	1	1	trivial
1600.4.a.n		1	20.d	odd	2	1
1600.4.a.bn		1	5.b	even	2	1
1600.4.a.bo		1	4.b	odd	2	1
1800.4.a.p		1	120.i	odd	2	1
1800.4.a.t		1	24.h	odd	2	1
1800.4.f.c		2	120.w	even	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1600))$:

$T_{3} + 5$

$T_{7} - 2$

$T_{11} + 39$

$T_{13} + 84$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T + 5$
$5$	$T$
$7$	$T - 2$
$11$	$T + 39$