Newform orbit 832.4.a.s

• Label: 832.4.a.s
• Level: $832$
• Weight: $4$
• Character orbit: 832.a
• Self dual: yes
• Analytic conductor: $49.090$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$832 = 2^{6} \cdot 13$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	832.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$49.0895891248$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17})$
Defining polynomial:	$x^{2} - x - 4$
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = \frac{1}{2}(1 + \sqrt{17})$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q + (-3*b - 1) * q^3 + (b + 1) * q^5 + (-11*b + 1) * q^7 + (15*b + 10) * q^9 + (12*b - 46) * q^11 + 13 * q^13 + (-7*b - 13) * q^15 + (17*b + 1) * q^17 + (-32*b + 58) * q^19 + (41*b + 131) * q^21 + (12*b + 92) * q^23 + (3*b - 120) * q^25 + (-9*b - 163) * q^27 + (96*b - 26) * q^29 + (34*b - 60) * q^31 + (90*b - 98) * q^33 + (-21*b - 43) * q^35 + (5*b - 107) * q^37 + (-39*b - 13) * q^39 + (-22*b - 104) * q^41 + (143*b - 215) * q^43 + (40*b + 70) * q^45 + (121*b + 157) * q^47 + (99*b + 142) * q^49 + (-71*b - 205) * q^51 + (30*b + 44) * q^53 + (-22*b + 2) * q^55 + (-46*b + 326) * q^57 + (124*b + 122) * q^59 + (-190*b + 624) * q^61 + (-260*b - 650) * q^63 + (13*b + 13) * q^65 + (-232*b + 82) * q^67 + (-324*b - 236) * q^69 + (231*b - 181) * q^71 + (-260*b + 358) * q^73 + (348*b + 84) * q^75 + (386*b - 574) * q^77 + (-40*b - 484) * q^79 + (120*b + 1) * q^81 + (-182*b - 888) * q^83 + (35*b + 69) * q^85 + (-306*b - 1126) * q^87 + (388*b - 554) * q^89 + (-143*b + 13) * q^91 + (44*b - 348) * q^93 + (-6*b - 70) * q^95 + (-508*b - 210) * q^97 + (-390*b + 260) * q^99
$\operatorname{Tr}(f)(q)$	$=$	2 * q - 5 * q^3 + 3 * q^5 - 9 * q^7 + 35 * q^9 - 80 * q^11 + 26 * q^13 - 33 * q^15 + 19 * q^17 + 84 * q^19 + 303 * q^21 + 196 * q^23 - 237 * q^25 - 335 * q^27 + 44 * q^29 - 86 * q^31 - 106 * q^33 - 107 * q^35 - 209 * q^37 - 65 * q^39 - 230 * q^41 - 287 * q^43 + 180 * q^45 + 435 * q^47 + 383 * q^49 - 481 * q^51 + 118 * q^53 - 18 * q^55 + 606 * q^57 + 368 * q^59 + 1058 * q^61 - 1560 * q^63 + 39 * q^65 - 68 * q^67 - 796 * q^69 - 131 * q^71 + 456 * q^73 + 516 * q^75 - 762 * q^77 - 1008 * q^79 + 122 * q^81 - 1958 * q^83 + 173 * q^85 - 2558 * q^87 - 720 * q^89 - 117 * q^91 - 652 * q^93 - 146 * q^95 - 928 * q^97 + 130 * 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

2.56155
−1.56155

0

−8.68466

0

3.56155

0

−27.1771

0

48.4233

0

1.2

0

3.68466

0

−0.561553

0

18.1771

0

−13.4233

0

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$13$	$-1$

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	832.4.a.s		2
4.b	odd	2	1		832.4.a.z		2
8.b	even	2	1		13.4.a.b	✓	2
8.d	odd	2	1		208.4.a.h		2
24.f	even	2	1		1872.4.a.bb		2
24.h	odd	2	1		117.4.a.d		2
40.f	even	2	1		325.4.a.f		2
40.i	odd	4	2		325.4.b.e		4
56.h	odd	2	1		637.4.a.b		2
88.b	odd	2	1		1573.4.a.b		2
104.e	even	2	1		169.4.a.g		2
104.j	odd	4	2		169.4.b.f		4
104.r	even	6	2		169.4.c.g		4
104.s	even	6	2		169.4.c.j		4
104.x	odd	12	4		169.4.e.f		8
312.b	odd	2	1		1521.4.a.r		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
13.4.a.b	✓	2	8.b	even	2	1
117.4.a.d		2	24.h	odd	2	1
169.4.a.g		2	104.e	even	2	1
169.4.b.f		4	104.j	odd	4	2
169.4.c.g		4	104.r	even	6	2
169.4.c.j		4	104.s	even	6	2
169.4.e.f		8	104.x	odd	12	4
208.4.a.h		2	8.d	odd	2	1
325.4.a.f		2	40.f	even	2	1
325.4.b.e		4	40.i	odd	4	2
637.4.a.b		2	56.h	odd	2	1
832.4.a.s		2	1.a	even	1	1	trivial
832.4.a.z		2	4.b	odd	2	1
1521.4.a.r		2	312.b	odd	2	1
1573.4.a.b		2	88.b	odd	2	1
1872.4.a.bb		2	24.f	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(832))$:

$T_{3}^{2} + 5T_{3} - 32$

$T_{5}^{2} - 3T_{5} - 2$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2}$
$3$	$T^{2} + 5T - 32$
$5$	$T^{2} - 3T - 2$
$7$	$T^{2} + 9T - 494$
$11$	$T^{2} + 80T + 988$