Newform orbit 17.4.a.a

• Label: 17.4.a.a
• Level: $17$
• Weight: $4$
• Character orbit: 17.a
• Self dual: yes
• Analytic conductor: $1.003$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$17$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	17.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$1.00303247010$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 3 * q^2 - 8 * q^3 + q^4 + 6 * q^5 + 24 * q^6 - 28 * q^7 + 21 * q^8 + 37 * q^9 - 18 * q^10 - 24 * q^11 - 8 * q^12 - 58 * q^13 + 84 * q^14 - 48 * q^15 - 71 * q^16 + 17 * q^17 - 111 * q^18 + 116 * q^19 + 6 * q^20 + 224 * q^21 + 72 * q^22 - 60 * q^23 - 168 * q^24 - 89 * q^25 + 174 * q^26 - 80 * q^27 - 28 * q^28 + 30 * q^29 + 144 * q^30 - 172 * q^31 + 45 * q^32 + 192 * q^33 - 51 * q^34 - 168 * q^35 + 37 * q^36 - 58 * q^37 - 348 * q^38 + 464 * q^39 + 126 * q^40 - 342 * q^41 - 672 * q^42 - 148 * q^43 - 24 * q^44 + 222 * q^45 + 180 * q^46 + 288 * q^47 + 568 * q^48 + 441 * q^49 + 267 * q^50 - 136 * q^51 - 58 * q^52 + 318 * q^53 + 240 * q^54 - 144 * q^55 - 588 * q^56 - 928 * q^57 - 90 * q^58 + 252 * q^59 - 48 * q^60 + 110 * q^61 + 516 * q^62 - 1036 * q^63 + 433 * q^64 - 348 * q^65 - 576 * q^66 - 484 * q^67 + 17 * q^68 + 480 * q^69 + 504 * q^70 - 708 * q^71 + 777 * q^72 + 362 * q^73 + 174 * q^74 + 712 * q^75 + 116 * q^76 + 672 * q^77 - 1392 * q^78 - 484 * q^79 - 426 * q^80 - 359 * q^81 + 1026 * q^82 + 756 * q^83 + 224 * q^84 + 102 * q^85 + 444 * q^86 - 240 * q^87 - 504 * q^88 - 774 * q^89 - 666 * q^90 + 1624 * q^91 - 60 * q^92 + 1376 * q^93 - 864 * q^94 + 696 * q^95 - 360 * q^96 - 382 * q^97 - 1323 * q^98 - 888 * 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

−3.00000

−8.00000

1.00000

6.00000

24.0000

−28.0000

21.0000

37.0000

−18.0000

Atkin-Lehner signs

$p$	Sign
$17$	$-1$

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	17.4.a.a	✓	1
3.b	odd	2	1		153.4.a.d		1
4.b	odd	2	1		272.4.a.d		1
5.b	even	2	1		425.4.a.d		1
5.c	odd	4	2		425.4.b.c		2
7.b	odd	2	1		833.4.a.a		1
8.b	even	2	1		1088.4.a.l		1
8.d	odd	2	1		1088.4.a.a		1
11.b	odd	2	1		2057.4.a.d		1
12.b	even	2	1		2448.4.a.f		1
17.b	even	2	1		289.4.a.a		1
17.c	even	4	2		289.4.b.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
17.4.a.a	✓	1	1.a	even	1	1	trivial
153.4.a.d		1	3.b	odd	2	1
272.4.a.d		1	4.b	odd	2	1
289.4.a.a		1	17.b	even	2	1
289.4.b.a		2	17.c	even	4	2
425.4.a.d		1	5.b	even	2	1
425.4.b.c		2	5.c	odd	4	2
833.4.a.a		1	7.b	odd	2	1
1088.4.a.a		1	8.d	odd	2	1
1088.4.a.l		1	8.b	even	2	1
2057.4.a.d		1	11.b	odd	2	1
2448.4.a.f		1	12.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2} + 3$ acting on $S_{4}^{\mathrm{new}}(\Gamma_0(17))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 3$
$3$	$T + 8$
$5$	$T - 6$
$7$	$T + 28$
$11$	$T + 24$