LMFDB - Newform orbit 650.4.a.c

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,4,Mod(1,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, 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("650.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	650.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:	$38.3512415037$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
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} + q^{3} + 4 q^{4} - 2 q^{6} + 35 q^{7} - 8 q^{8} - 26 q^{9}+O(q^{10}) $

$ q - 2 q^{2} + q^{3} + 4 q^{4} - 2 q^{6} + 35 q^{7} - 8 q^{8} - 26 q^{9} + 2 q^{11} + 4 q^{12} - 13 q^{13} - 70 q^{14} + 16 q^{16} + 19 q^{17} + 52 q^{18} + 94 q^{19} + 35 q^{21} - 4 q^{22} + 72 q^{23} - 8 q^{24} + 26 q^{26} - 53 q^{27} + 140 q^{28} + 246 q^{29} - 100 q^{31} - 32 q^{32} + 2 q^{33} - 38 q^{34} - 104 q^{36} + 11 q^{37} - 188 q^{38} - 13 q^{39} - 280 q^{41} - 70 q^{42} - 241 q^{43} + 8 q^{44} - 144 q^{46} - 137 q^{47} + 16 q^{48} + 882 q^{49} + 19 q^{51} - 52 q^{52} + 232 q^{53} + 106 q^{54} - 280 q^{56} + 94 q^{57} - 492 q^{58} - 386 q^{59} + 64 q^{61} + 200 q^{62} - 910 q^{63} + 64 q^{64} - 4 q^{66} + 670 q^{67} + 76 q^{68} + 72 q^{69} + 55 q^{71} + 208 q^{72} + 838 q^{73} - 22 q^{74} + 376 q^{76} + 70 q^{77} + 26 q^{78} + 1016 q^{79} + 649 q^{81} + 560 q^{82} - 420 q^{83} + 140 q^{84} + 482 q^{86} + 246 q^{87} - 16 q^{88} - 934 q^{89} - 455 q^{91} + 288 q^{92} - 100 q^{93} + 274 q^{94} - 32 q^{96} + 1154 q^{97} - 1764 q^{98} - 52 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

1.00000

4.00000

−2.00000

35.0000

−8.00000

−26.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ +1 $
$5$	$ +1 $
$13$	$ +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	650.4.a.c		1
5.b	even	2	1		26.4.a.b	✓	1
5.c	odd	4	2		650.4.b.d		2
15.d	odd	2	1		234.4.a.a		1
20.d	odd	2	1		208.4.a.e		1
35.c	odd	2	1		1274.4.a.f		1
40.e	odd	2	1		832.4.a.g		1
40.f	even	2	1		832.4.a.j		1
60.h	even	2	1		1872.4.a.b		1
65.d	even	2	1		338.4.a.b		1
65.g	odd	4	2		338.4.b.b		2
65.l	even	6	2		338.4.c.g		2
65.n	even	6	2		338.4.c.c		2
65.s	odd	12	4		338.4.e.c		4

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
26.4.a.b	✓	1	5.b	even	2	1
208.4.a.e		1	20.d	odd	2	1
234.4.a.a		1	15.d	odd	2	1
338.4.a.b		1	65.d	even	2	1
338.4.b.b		2	65.g	odd	4	2
338.4.c.c		2	65.n	even	6	2
338.4.c.g		2	65.l	even	6	2
338.4.e.c		4	65.s	odd	12	4
650.4.a.c		1	1.a	even	1	1	trivial
650.4.b.d		2	5.c	odd	4	2
832.4.a.g		1	40.e	odd	2	1
832.4.a.j		1	40.f	even	2	1
1274.4.a.f		1	35.c	odd	2	1
1872.4.a.b		1	60.h	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(650))$:

$ T_{3} - 1 $

$ T_{7} - 35 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 2 $ T + 2
$3$	$ T - 1 $ T - 1
$5$	$ T $ T
$7$	$ T - 35 $ T - 35
$11$	$ T - 2 $ T - 2
$13$	$ T + 13 $ T + 13
$17$	$ T - 19 $ T - 19
$19$	$ T - 94 $ T - 94
$23$	$ T - 72 $ T - 72
$29$	$ T - 246 $ T - 246
$31$	$ T + 100 $ T + 100
$37$	$ T - 11 $ T - 11
$41$	$ T + 280 $ T + 280
$43$	$ T + 241 $ T + 241
$47$	$ T + 137 $ T + 137
$53$	$ T - 232 $ T - 232
$59$	$ T + 386 $ T + 386
$61$	$ T - 64 $ T - 64
$67$	$ T - 670 $ T - 670
$71$	$ T - 55 $ T - 55
$73$	$ T - 838 $ T - 838
$79$	$ T - 1016 $ T - 1016
$83$	$ T + 420 $ T + 420
$89$	$ T + 934 $ T + 934
$97$	$ T - 1154 $ T - 1154
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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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	650.a (trivial)

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