Newform orbit 147.6.a.d

• Label: 147.6.a.d
• Level: $147$
• Weight: $6$
• Character orbit: 147.a
• Self dual: yes
• Analytic conductor: $23.576$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$147 = 3 \cdot 7^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	147.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$23.5764215125$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 21)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 2 * q^2 + 9 * q^3 - 28 * q^4 - 11 * q^5 - 18 * q^6 + 120 * q^8 + 81 * q^9 + 22 * q^10 + 269 * q^11 - 252 * q^12 + 308 * q^13 - 99 * q^15 + 656 * q^16 - 1896 * q^17 - 162 * q^18 + 164 * q^19 + 308 * q^20 - 538 * q^22 - 3264 * q^23 + 1080 * q^24 - 3004 * q^25 - 616 * q^26 + 729 * q^27 + 2417 * q^29 + 198 * q^30 - 2841 * q^31 - 5152 * q^32 + 2421 * q^33 + 3792 * q^34 - 2268 * q^36 - 11328 * q^37 - 328 * q^38 + 2772 * q^39 - 1320 * q^40 + 16856 * q^41 - 7894 * q^43 - 7532 * q^44 - 891 * q^45 + 6528 * q^46 - 21102 * q^47 + 5904 * q^48 + 6008 * q^50 - 17064 * q^51 - 8624 * q^52 - 29691 * q^53 - 1458 * q^54 - 2959 * q^55 + 1476 * q^57 - 4834 * q^58 + 8163 * q^59 + 2772 * q^60 - 15166 * q^61 + 5682 * q^62 - 10688 * q^64 - 3388 * q^65 - 4842 * q^66 - 32078 * q^67 + 53088 * q^68 - 29376 * q^69 - 38274 * q^71 + 9720 * q^72 - 34866 * q^73 + 22656 * q^74 - 27036 * q^75 - 4592 * q^76 - 5544 * q^78 + 13529 * q^79 - 7216 * q^80 + 6561 * q^81 - 33712 * q^82 + 68103 * q^83 + 20856 * q^85 + 15788 * q^86 + 21753 * q^87 + 32280 * q^88 + 114922 * q^89 + 1782 * q^90 + 91392 * q^92 - 25569 * q^93 + 42204 * q^94 - 1804 * q^95 - 46368 * q^96 - 154959 * q^97 + 21789 * 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

−2.00000

9.00000

−28.0000

−11.0000

−18.0000

0

120.000

81.0000

22.0000

Atkin-Lehner signs

$p$	Sign
$3$	$-1$
$7$	$-1$

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	147.6.a.d		1
3.b	odd	2	1		441.6.a.h		1
7.b	odd	2	1		147.6.a.c		1
7.c	even	3	2		147.6.e.g		2
7.d	odd	6	2		21.6.e.a	✓	2
21.c	even	2	1		441.6.a.g		1
21.g	even	6	2		63.6.e.a		2
28.f	even	6	2		336.6.q.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
21.6.e.a	✓	2	7.d	odd	6	2
63.6.e.a		2	21.g	even	6	2
147.6.a.c		1	7.b	odd	2	1
147.6.a.d		1	1.a	even	1	1	trivial
147.6.e.g		2	7.c	even	3	2
336.6.q.b		2	28.f	even	6	2
441.6.a.g		1	21.c	even	2	1
441.6.a.h		1	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{6}^{\mathrm{new}}(\Gamma_0(147))$:

$T_{2} + 2$

$T_{5} + 11$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 2$
$3$	$T - 9$
$5$	$T + 11$
$7$	$T$
$11$	$T - 269$