Newform orbit 350.4.a.v

• Label: 350.4.a.v
• Level: $350$
• Weight: $4$
• Character orbit: 350.a
• Self dual: yes
• Analytic conductor: $20.651$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$350 = 2 \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	350.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 2 * q^2 + 8 * q^3 + 4 * q^4 + 16 * q^6 + 7 * q^7 + 8 * q^8 + 37 * q^9 + 68 * q^11 + 32 * q^12 - 34 * q^13 + 14 * q^14 + 16 * q^16 - 74 * q^17 + 74 * q^18 - 128 * q^19 + 56 * q^21 + 136 * q^22 + 80 * q^23 + 64 * q^24 - 68 * q^26 + 80 * q^27 + 28 * q^28 + 286 * q^29 - 24 * q^31 + 32 * q^32 + 544 * q^33 - 148 * q^34 + 148 * q^36 - 294 * q^37 - 256 * q^38 - 272 * q^39 + 66 * q^41 + 112 * q^42 + 124 * q^43 + 272 * q^44 + 160 * q^46 - 312 * q^47 + 128 * q^48 + 49 * q^49 - 592 * q^51 - 136 * q^52 + 34 * q^53 + 160 * q^54 + 56 * q^56 - 1024 * q^57 + 572 * q^58 + 168 * q^59 + 170 * q^61 - 48 * q^62 + 259 * q^63 + 64 * q^64 + 1088 * q^66 - 564 * q^67 - 296 * q^68 + 640 * q^69 + 616 * q^71 + 296 * q^72 - 250 * q^73 - 588 * q^74 - 512 * q^76 + 476 * q^77 - 544 * q^78 - 944 * q^79 - 359 * q^81 + 132 * q^82 - 672 * q^83 + 224 * q^84 + 248 * q^86 + 2288 * q^87 + 544 * q^88 - 1430 * q^89 - 238 * q^91 + 320 * q^92 - 192 * q^93 - 624 * q^94 + 256 * q^96 + 1270 * q^97 + 98 * q^98 + 2516 * 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

8.00000

4.00000

0

16.0000

7.00000

8.00000

37.0000

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$5$	$+1$
$7$	$-1$

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	350.4.a.v		1
5.b	even	2	1		70.4.a.a	✓	1
5.c	odd	4	2		350.4.c.n		2
7.b	odd	2	1		2450.4.a.x		1
15.d	odd	2	1		630.4.a.s		1
20.d	odd	2	1		560.4.a.q		1
35.c	odd	2	1		490.4.a.g		1
35.i	odd	6	2		490.4.e.j		2
35.j	even	6	2		490.4.e.r		2
40.e	odd	2	1		2240.4.a.d		1
40.f	even	2	1		2240.4.a.bi		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.4.a.a	✓	1	5.b	even	2	1
350.4.a.v		1	1.a	even	1	1	trivial
350.4.c.n		2	5.c	odd	4	2
490.4.a.g		1	35.c	odd	2	1
490.4.e.j		2	35.i	odd	6	2
490.4.e.r		2	35.j	even	6	2
560.4.a.q		1	20.d	odd	2	1
630.4.a.s		1	15.d	odd	2	1
2240.4.a.d		1	40.e	odd	2	1
2240.4.a.bi		1	40.f	even	2	1
2450.4.a.x		1	7.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 $S_{4}^{\mathrm{new}}(\Gamma_0(350))$:

$T_{3} - 8$

$T_{11} - 68$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 2$
$3$	$T - 8$
$5$	$T$
$7$	$T - 7$
$11$	$T - 68$