Newform orbit 882.6.a.bh

• Label: 882.6.a.bh
• Level: $882$
• Weight: $6$
• Character orbit: 882.a
• Self dual: yes
• Analytic conductor: $141.459$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$882 = 2 \cdot 3^{2} \cdot 7^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	882.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$141.458529075$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{9601})$
Defining polynomial:	$x^{2} - x - 2400$
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 42)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = \frac{1}{2}(1 + \sqrt{9601})$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q - 4 * q^2 + 16 * q^4 + (-b + 27) * q^5 - 64 * q^8 + (4*b - 108) * q^10 + (-5*b - 93) * q^11 + (-11*b - 184) * q^13 + 256 * q^16 + (-20*b + 180) * q^17 + (39*b - 904) * q^19 + (-16*b + 432) * q^20 + (20*b + 372) * q^22 + (4*b - 1620) * q^23 + (-53*b + 4) * q^25 + (44*b + 736) * q^26 + (-61*b - 2199) * q^29 + (-164*b + 1079) * q^31 - 1024 * q^32 + (80*b - 720) * q^34 + (51*b + 10268) * q^37 + (-156*b + 3616) * q^38 + (64*b - 1728) * q^40 + (66*b - 4440) * q^41 + (-87*b + 7970) * q^43 + (-80*b - 1488) * q^44 + (-16*b + 6480) * q^46 + (156*b - 17034) * q^47 + (212*b - 16) * q^50 + (-176*b - 2944) * q^52 + (-225*b - 24507) * q^53 + (-37*b + 9489) * q^55 + (244*b + 8796) * q^58 + (41*b + 28347) * q^59 + (-32*b + 33770) * q^61 + (656*b - 4316) * q^62 + 4096 * q^64 + (-102*b + 21432) * q^65 + (-337*b + 38030) * q^67 + (-320*b + 2880) * q^68 + (-1340*b + 5166) * q^71 + (875*b - 2038) * q^73 + (-204*b - 41072) * q^74 + (624*b - 14464) * q^76 + (-986*b + 13799) * q^79 + (-256*b + 6912) * q^80 + (-264*b + 17760) * q^82 + (-1769*b + 1359) * q^83 + (-700*b + 52860) * q^85 + (348*b - 31880) * q^86 + (320*b + 5952) * q^88 + (210*b - 88386) * q^89 + (64*b - 25920) * q^92 + (-624*b + 68136) * q^94 + (1918*b - 118008) * q^95 + (-1981*b - 63721) * q^97
$\operatorname{Tr}(f)(q)$	$=$	2 * q - 8 * q^2 + 32 * q^4 + 53 * q^5 - 128 * q^8 - 212 * q^10 - 191 * q^11 - 379 * q^13 + 512 * q^16 + 340 * q^17 - 1769 * q^19 + 848 * q^20 + 764 * q^22 - 3236 * q^23 - 45 * q^25 + 1516 * q^26 - 4459 * q^29 + 1994 * q^31 - 2048 * q^32 - 1360 * q^34 + 20587 * q^37 + 7076 * q^38 - 3392 * q^40 - 8814 * q^41 + 15853 * q^43 - 3056 * q^44 + 12944 * q^46 - 33912 * q^47 + 180 * q^50 - 6064 * q^52 - 49239 * q^53 + 18941 * q^55 + 17836 * q^58 + 56735 * q^59 + 67508 * q^61 - 7976 * q^62 + 8192 * q^64 + 42762 * q^65 + 75723 * q^67 + 5440 * q^68 + 8992 * q^71 - 3201 * q^73 - 82348 * q^74 - 28304 * q^76 + 26612 * q^79 + 13568 * q^80 + 35256 * q^82 + 949 * q^83 + 105020 * q^85 - 63412 * q^86 + 12224 * q^88 - 176562 * q^89 - 51776 * q^92 + 135648 * q^94 - 234098 * q^95 - 129423 * 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

49.4923
−48.4923

−4.00000

0

16.0000

−22.4923

0

0

−64.0000

0

89.9694

1.2

−4.00000

0

16.0000

75.4923

0

0

−64.0000

0

−301.969

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$-1$
$7$	$+1$

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	882.6.a.bh		2
3.b	odd	2	1		294.6.a.r		2
7.b	odd	2	1		882.6.a.bb		2
7.c	even	3	2		126.6.g.h		4
21.c	even	2	1		294.6.a.w		2
21.g	even	6	2		294.6.e.s		4
21.h	odd	6	2		42.6.e.c	✓	4
84.n	even	6	2		336.6.q.f		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
42.6.e.c	✓	4	21.h	odd	6	2
126.6.g.h		4	7.c	even	3	2
294.6.a.r		2	3.b	odd	2	1
294.6.a.w		2	21.c	even	2	1
294.6.e.s		4	21.g	even	6	2
336.6.q.f		4	84.n	even	6	2
882.6.a.bb		2	7.b	odd	2	1
882.6.a.bh		2	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{6}^{\mathrm{new}}(\Gamma_0(882))$:

$T_{5}^{2} - 53T_{5} - 1698$

$T_{11}^{2} + 191T_{11} - 50886$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$(T + 4)^{2}$
$3$	$T^{2}$
$5$	$T^{2} - 53T - 1698$
$7$	$T^{2}$
$11$	$T^{2} + 191T - 50886$