LMFDB - Newform orbit 350.4.a.v

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(1,350)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("350.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$ q + 2 q^{2} + 8 q^{3} + 4 q^{4} + 16 q^{6} + 7 q^{7} + 8 q^{8} + 37 q^{9}+O(q^{10}) $

$ 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}+O(q^{100}) $

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label

$\iota_m(\nu)$

$ a_{2} $

$ a_{3} $

$ a_{4} $

$ a_{5} $

$ a_{6} $

$ a_{7} $

$ a_{8} $

$ a_{9} $

$ a_{10} $

1.1

2.00000

8.00000

4.00000

16.0000

7.00000

8.00000

37.0000

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 $ T - 2
$3$	$ T - 8 $ T - 8
$5$	$ T $ T
$7$	$ T - 7 $ T - 7
$11$	$ T - 68 $ T - 68
$13$	$ T + 34 $ T + 34
$17$	$ T + 74 $ T + 74
$19$	$ T + 128 $ T + 128
$23$	$ T - 80 $ T - 80
$29$	$ T - 286 $ T - 286
$31$	$ T + 24 $ T + 24
$37$	$ T + 294 $ T + 294
$41$	$ T - 66 $ T - 66
$43$	$ T - 124 $ T - 124
$47$	$ T + 312 $ T + 312
$53$	$ T - 34 $ T - 34
$59$	$ T - 168 $ T - 168
$61$	$ T - 170 $ T - 170
$67$	$ T + 564 $ T + 564
$71$	$ T - 616 $ T - 616
$73$	$ T + 250 $ T + 250
$79$	$ T + 944 $ T + 944
$83$	$ T + 672 $ T + 672
$89$	$ T + 1430 $ T + 1430
$97$	$ T - 1270 $ T - 1270
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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
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