Newform orbit 2156.4.a.d

• Label: 2156.4.a.d
• Level: $2156$
• Weight: $4$
• Character orbit: 2156.a
• Self dual: yes
• Analytic conductor: $127.208$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$2156 = 2^{2} \cdot 7^{2} \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	2156.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$127.208117972$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{97})$
Defining polynomial:	$x^{2} - x - 24$
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 44)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = \frac{1}{2}(1 + \sqrt{97})$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q + (-b - 4) * q^3 + (b - 6) * q^5 + (9*b + 13) * q^9 + 11 * q^11 + (2*b + 10) * q^13 + b * q^15 + (4*b + 78) * q^17 + (-20*b + 4) * q^19 + (-23*b - 48) * q^23 + (-11*b - 65) * q^25 + (-31*b - 160) * q^27 + (42*b - 90) * q^29 + (-b - 200) * q^31 + (-11*b - 44) * q^33 + (-23*b + 182) * q^37 + (-20*b - 88) * q^39 + (18*b + 150) * q^41 + (26*b + 212) * q^43 + (-32*b + 138) * q^45 + (-72*b + 192) * q^47 + (-98*b - 408) * q^51 + (20*b - 210) * q^53 + (11*b - 66) * q^55 + (96*b + 464) * q^57 + (-51*b + 36) * q^59 + (-38*b + 250) * q^61 - 12 * q^65 + (95*b + 116) * q^67 + (163*b + 744) * q^69 + (-69*b + 336) * q^71 + (-58*b - 74) * q^73 + (120*b + 524) * q^75 + (42*b + 992) * q^79 + (72*b + 1033) * q^81 + (-82*b + 564) * q^83 + (58*b - 372) * q^85 + (-120*b - 648) * q^87 + (179*b - 450) * q^89 + (205*b + 824) * q^93 + (104*b - 504) * q^95 + (217*b - 842) * q^97 + (99*b + 143) * q^99
$\operatorname{Tr}(f)(q)$	$=$	2 * q - 9 * q^3 - 11 * q^5 + 35 * q^9 + 22 * q^11 + 22 * q^13 + q^15 + 160 * q^17 - 12 * q^19 - 119 * q^23 - 141 * q^25 - 351 * q^27 - 138 * q^29 - 401 * q^31 - 99 * q^33 + 341 * q^37 - 196 * q^39 + 318 * q^41 + 450 * q^43 + 244 * q^45 + 312 * q^47 - 914 * q^51 - 400 * q^53 - 121 * q^55 + 1024 * q^57 + 21 * q^59 + 462 * q^61 - 24 * q^65 + 327 * q^67 + 1651 * q^69 + 603 * q^71 - 206 * q^73 + 1168 * q^75 + 2026 * q^79 + 2138 * q^81 + 1046 * q^83 - 686 * q^85 - 1416 * q^87 - 721 * q^89 + 1853 * q^93 - 904 * q^95 - 1467 * q^97 + 385 * 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

5.42443
−4.42443

0

−9.42443

0

−0.575571

0

0

0

61.8199

0

1.2

0

0.424429

0

−10.4244

0

0

0

−26.8199

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$7$	$-1$
$11$	$-1$

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	2156.4.a.d		2
7.b	odd	2	1		44.4.a.b	✓	2
21.c	even	2	1		396.4.a.i		2
28.d	even	2	1		176.4.a.g		2
35.c	odd	2	1		1100.4.a.e		2
35.f	even	4	2		1100.4.b.e		4
56.e	even	2	1		704.4.a.r		2
56.h	odd	2	1		704.4.a.m		2
77.b	even	2	1		484.4.a.e		2
84.h	odd	2	1		1584.4.a.z		2
308.g	odd	2	1		1936.4.a.o		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
44.4.a.b	✓	2	7.b	odd	2	1
176.4.a.g		2	28.d	even	2	1
396.4.a.i		2	21.c	even	2	1
484.4.a.e		2	77.b	even	2	1
704.4.a.m		2	56.h	odd	2	1
704.4.a.r		2	56.e	even	2	1
1100.4.a.e		2	35.c	odd	2	1
1100.4.b.e		4	35.f	even	4	2
1584.4.a.z		2	84.h	odd	2	1
1936.4.a.o		2	308.g	odd	2	1
2156.4.a.d		2	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3}^{2} + 9T_{3} - 4$ acting on $S_{4}^{\mathrm{new}}(\Gamma_0(2156))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2}$
$3$	$T^{2} + 9T - 4$
$5$	$T^{2} + 11T + 6$
$7$	$T^{2}$
$11$	$(T - 11)^{2}$