LMFDB - Newform orbit 2450.4.a.d

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 14)
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} - 5 q^{3} + 4 q^{4} + 10 q^{6} - 8 q^{8} - 2 q^{9}+O(q^{10}) $

$ q - 2 q^{2} - 5 q^{3} + 4 q^{4} + 10 q^{6} - 8 q^{8} - 2 q^{9} - 57 q^{11} - 20 q^{12} - 70 q^{13} + 16 q^{16} + 51 q^{17} + 4 q^{18} - 5 q^{19} + 114 q^{22} - 69 q^{23} + 40 q^{24} + 140 q^{26} + 145 q^{27} + 114 q^{29} - 23 q^{31} - 32 q^{32} + 285 q^{33} - 102 q^{34} - 8 q^{36} + 253 q^{37} + 10 q^{38} + 350 q^{39} + 42 q^{41} + 124 q^{43} - 228 q^{44} + 138 q^{46} + 201 q^{47} - 80 q^{48} - 255 q^{51} - 280 q^{52} + 393 q^{53} - 290 q^{54} + 25 q^{57} - 228 q^{58} - 219 q^{59} + 709 q^{61} + 46 q^{62} + 64 q^{64} - 570 q^{66} - 419 q^{67} + 204 q^{68} + 345 q^{69} - 96 q^{71} + 16 q^{72} - 313 q^{73} - 506 q^{74} - 20 q^{76} - 700 q^{78} + 461 q^{79} - 671 q^{81} - 84 q^{82} - 588 q^{83} - 248 q^{86} - 570 q^{87} + 456 q^{88} + 1017 q^{89} - 276 q^{92} + 115 q^{93} - 402 q^{94} + 160 q^{96} - 1834 q^{97} + 114 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

−5.00000

4.00000

10.0000

−8.00000

−2.00000

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.d		1
5.b	even	2	1		98.4.a.f		1
7.b	odd	2	1		2450.4.a.q		1
7.d	odd	6	2		350.4.e.e		2
15.d	odd	2	1		882.4.a.c		1
20.d	odd	2	1		784.4.a.c		1
35.c	odd	2	1		98.4.a.d		1
35.i	odd	6	2		14.4.c.a	✓	2
35.j	even	6	2		98.4.c.a		2
35.k	even	12	4		350.4.j.b		4
105.g	even	2	1		882.4.a.f		1
105.o	odd	6	2		882.4.g.u		2
105.p	even	6	2		126.4.g.d		2
140.c	even	2	1		784.4.a.p		1
140.s	even	6	2		112.4.i.a		2
280.ba	even	6	2		448.4.i.e		2
280.bk	odd	6	2		448.4.i.b		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
14.4.c.a	✓	2	35.i	odd	6	2
98.4.a.d		1	35.c	odd	2	1
98.4.a.f		1	5.b	even	2	1
98.4.c.a		2	35.j	even	6	2
112.4.i.a		2	140.s	even	6	2
126.4.g.d		2	105.p	even	6	2
350.4.e.e		2	7.d	odd	6	2
350.4.j.b		4	35.k	even	12	4
448.4.i.b		2	280.bk	odd	6	2
448.4.i.e		2	280.ba	even	6	2
784.4.a.c		1	20.d	odd	2	1
784.4.a.p		1	140.c	even	2	1
882.4.a.c		1	15.d	odd	2	1
882.4.a.f		1	105.g	even	2	1
882.4.g.u		2	105.o	odd	6	2
2450.4.a.d		1	1.a	even	1	1	trivial
2450.4.a.q		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} + 5 $

$ T_{11} + 57 $

$ T_{19} + 5 $

$ T_{23} + 69 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 2 $ T + 2
$3$	$ T + 5 $ T + 5
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T + 57 $ T + 57
$13$	$ T + 70 $ T + 70
$17$	$ T - 51 $ T - 51
$19$	$ T + 5 $ T + 5
$23$	$ T + 69 $ T + 69
$29$	$ T - 114 $ T - 114
$31$	$ T + 23 $ T + 23
$37$	$ T - 253 $ T - 253
$41$	$ T - 42 $ T - 42
$43$	$ T - 124 $ T - 124
$47$	$ T - 201 $ T - 201
$53$	$ T - 393 $ T - 393
$59$	$ T + 219 $ T + 219
$61$	$ T - 709 $ T - 709
$67$	$ T + 419 $ T + 419
$71$	$ T + 96 $ T + 96
$73$	$ T + 313 $ T + 313
$79$	$ T - 461 $ T - 461
$83$	$ T + 588 $ T + 588
$89$	$ T - 1017 $ T - 1017
$97$	$ T + 1834 $ T + 1834
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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:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2450.a (trivial)

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