LMFDB - Newform orbit 2450.4.a.v

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2450,4,Mod(1,2450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2450, 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("2450.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2450 = 2 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2450.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:	$144.554679514$
Analytic rank:	$1$
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} - 10 q^{3} + 4 q^{4} - 20 q^{6} + 8 q^{8} + 73 q^{9}+O(q^{10}) $

$ q + 2 q^{2} - 10 q^{3} + 4 q^{4} - 20 q^{6} + 8 q^{8} + 73 q^{9} + 53 q^{11} - 40 q^{12} - 25 q^{13} + 16 q^{16} - 14 q^{17} + 146 q^{18} - 95 q^{19} + 106 q^{22} - q^{23} - 80 q^{24} - 50 q^{26} - 460 q^{27} - 206 q^{29} + 108 q^{31} + 32 q^{32} - 530 q^{33} - 28 q^{34} + 292 q^{36} + 57 q^{37} - 190 q^{38} + 250 q^{39} + 243 q^{41} - 434 q^{43} + 212 q^{44} - 2 q^{46} + 231 q^{47} - 160 q^{48} + 140 q^{51} - 100 q^{52} - 263 q^{53} - 920 q^{54} + 950 q^{57} - 412 q^{58} + 24 q^{59} + 116 q^{61} + 216 q^{62} + 64 q^{64} - 1060 q^{66} + 204 q^{67} - 56 q^{68} + 10 q^{69} + 484 q^{71} + 584 q^{72} + 692 q^{73} + 114 q^{74} - 380 q^{76} + 500 q^{78} + 466 q^{79} + 2629 q^{81} + 486 q^{82} - 228 q^{83} - 868 q^{86} + 2060 q^{87} + 424 q^{88} - 362 q^{89} - 4 q^{92} - 1080 q^{93} + 462 q^{94} - 320 q^{96} - 854 q^{97} + 3869 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

−10.0000

4.00000

−20.0000

8.00000

73.0000

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	2450.4.a.v		1
5.b	even	2	1		490.4.a.h		1
7.b	odd	2	1		2450.4.a.bq		1
7.c	even	3	2		350.4.e.d		2
35.c	odd	2	1		490.4.a.a		1
35.i	odd	6	2		490.4.e.s		2
35.j	even	6	2		70.4.e.b	✓	2
35.l	odd	12	4		350.4.j.a		4
105.o	odd	6	2		630.4.k.c		2
140.p	odd	6	2		560.4.q.g		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.4.e.b	✓	2	35.j	even	6	2
350.4.e.d		2	7.c	even	3	2
350.4.j.a		4	35.l	odd	12	4
490.4.a.a		1	35.c	odd	2	1
490.4.a.h		1	5.b	even	2	1
490.4.e.s		2	35.i	odd	6	2
560.4.q.g		2	140.p	odd	6	2
630.4.k.c		2	105.o	odd	6	2
2450.4.a.v		1	1.a	even	1	1	trivial
2450.4.a.bq		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 $S_{4}^{\mathrm{new}}(\Gamma_0(2450))$:

$ T_{3} + 10 $

$ T_{11} - 53 $

$ T_{19} + 95 $

$ T_{23} + 1 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 2 $ T - 2
$3$	$ T + 10 $ T + 10
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T - 53 $ T - 53
$13$	$ T + 25 $ T + 25
$17$	$ T + 14 $ T + 14
$19$	$ T + 95 $ T + 95
$23$	$ T + 1 $ T + 1
$29$	$ T + 206 $ T + 206
$31$	$ T - 108 $ T - 108
$37$	$ T - 57 $ T - 57
$41$	$ T - 243 $ T - 243
$43$	$ T + 434 $ T + 434
$47$	$ T - 231 $ T - 231
$53$	$ T + 263 $ T + 263
$59$	$ T - 24 $ T - 24
$61$	$ T - 116 $ T - 116
$67$	$ T - 204 $ T - 204
$71$	$ T - 484 $ T - 484
$73$	$ T - 692 $ T - 692
$79$	$ T - 466 $ T - 466
$83$	$ T + 228 $ T + 228
$89$	$ T + 362 $ T + 362
$97$	$ T + 854 $ T + 854
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Overview	Random
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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2450.a (trivial)

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