Newform orbit 1872.4.a.t

• Label: 1872.4.a.t
• Level: $1872$
• Weight: $4$
• Character orbit: 1872.a
• Self dual: yes
• Analytic conductor: $110.452$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$1872 = 2^{4} \cdot 3^{2} \cdot 13$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1872.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$110.451575531$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{14})$
Defining polynomial:	$x^{2} - 14$
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2$
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = 2\sqrt{14}$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q + (b - 12) * q^5 + b * q^7 + (-6*b - 22) * q^11 - 13 * q^13 + (-2*b - 82) * q^17 + (-b - 24) * q^19 + (24*b + 4) * q^23 + (-24*b + 75) * q^25 + (12*b - 202) * q^29 + (13*b - 20) * q^31 + (-12*b + 56) * q^35 + (14*b - 50) * q^37 + (-47*b - 100) * q^41 + (-26*b + 308) * q^43 + (16*b - 162) * q^47 - 287 * q^49 + (60*b + 82) * q^53 + (50*b - 72) * q^55 + (20*b + 70) * q^59 + (68*b + 314) * q^61 + (-13*b + 156) * q^65 + (85*b + 236) * q^67 + (-42*b + 214) * q^71 + (38*b - 450) * q^73 + (-22*b - 336) * q^77 + (44*b + 216) * q^79 + (32*b - 694) * q^83 + (-58*b + 872) * q^85 + (95*b - 480) * q^89 - 13*b * q^91 + (-12*b + 232) * q^95 + (-110*b - 266) * q^97
$\operatorname{Tr}(f)(q)$	$=$	2 * q - 24 * q^5 - 44 * q^11 - 26 * q^13 - 164 * q^17 - 48 * q^19 + 8 * q^23 + 150 * q^25 - 404 * q^29 - 40 * q^31 + 112 * q^35 - 100 * q^37 - 200 * q^41 + 616 * q^43 - 324 * q^47 - 574 * q^49 + 164 * q^53 - 144 * q^55 + 140 * q^59 + 628 * q^61 + 312 * q^65 + 472 * q^67 + 428 * q^71 - 900 * q^73 - 672 * q^77 + 432 * q^79 - 1388 * q^83 + 1744 * q^85 - 960 * q^89 + 464 * q^95 - 532 * q^97

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

−3.74166
3.74166

0

0

0

−19.4833

0

−7.48331

0

0

0

1.2

0

0

0

−4.51669

0

7.48331

0

0

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$13$	$+1$

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	1872.4.a.t		2
3.b	odd	2	1		624.4.a.r		2
4.b	odd	2	1		117.4.a.c		2
12.b	even	2	1		39.4.a.b	✓	2
24.f	even	2	1		2496.4.a.bc		2
24.h	odd	2	1		2496.4.a.s		2
52.b	odd	2	1		1521.4.a.s		2
60.h	even	2	1		975.4.a.j		2
84.h	odd	2	1		1911.4.a.h		2
156.h	even	2	1		507.4.a.f		2
156.l	odd	4	2		507.4.b.f		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
39.4.a.b	✓	2	12.b	even	2	1
117.4.a.c		2	4.b	odd	2	1
507.4.a.f		2	156.h	even	2	1
507.4.b.f		4	156.l	odd	4	2
624.4.a.r		2	3.b	odd	2	1
975.4.a.j		2	60.h	even	2	1
1521.4.a.s		2	52.b	odd	2	1
1872.4.a.t		2	1.a	even	1	1	trivial
1911.4.a.h		2	84.h	odd	2	1
2496.4.a.s		2	24.h	odd	2	1
2496.4.a.bc		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 $S_{4}^{\mathrm{new}}(\Gamma_0(1872))$:

$T_{5}^{2} + 24T_{5} + 88$

$T_{7}^{2} - 56$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2}$
$3$	$T^{2}$
$5$	$T^{2} + 24T + 88$
$7$	$T^{2} - 56$
$11$	$T^{2} + 44T - 1532$