LMFDB - Newform orbit 2450.4.a.m

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} + q^{3} + 4 q^{4} - 2 q^{6} - 8 q^{8} - 26 q^{9}+O(q^{10}) $

$ q - 2 q^{2} + q^{3} + 4 q^{4} - 2 q^{6} - 8 q^{8} - 26 q^{9} - 30 q^{11} + 4 q^{12} + 44 q^{13} + 16 q^{16} - 24 q^{17} + 52 q^{18} - 2 q^{19} + 60 q^{22} + 183 q^{23} - 8 q^{24} - 88 q^{26} - 53 q^{27} - 279 q^{29} + 40 q^{31} - 32 q^{32} - 30 q^{33} + 48 q^{34} - 104 q^{36} + 76 q^{37} + 4 q^{38} + 44 q^{39} + 423 q^{41} - 305 q^{43} - 120 q^{44} - 366 q^{46} + 456 q^{47} + 16 q^{48} - 24 q^{51} + 176 q^{52} + 198 q^{53} + 106 q^{54} - 2 q^{57} + 558 q^{58} + 462 q^{59} - 281 q^{61} - 80 q^{62} + 64 q^{64} + 60 q^{66} + 499 q^{67} - 96 q^{68} + 183 q^{69} - 534 q^{71} + 208 q^{72} + 800 q^{73} - 152 q^{74} - 8 q^{76} - 88 q^{78} - 790 q^{79} + 649 q^{81} - 846 q^{82} - 597 q^{83} + 610 q^{86} - 279 q^{87} + 240 q^{88} - 1017 q^{89} + 732 q^{92} + 40 q^{93} - 912 q^{94} - 32 q^{96} - 1330 q^{97} + 780 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

−8.00000

−26.0000

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

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.4.e.a	✓	2	35.i	odd	6	2
350.4.e.g		2	7.d	odd	6	2
350.4.j.f		4	35.k	even	12	4
490.4.a.k		1	5.b	even	2	1
490.4.a.m		1	35.c	odd	2	1
490.4.e.f		2	35.j	even	6	2
560.4.q.e		2	140.s	even	6	2
630.4.k.i		2	105.p	even	6	2
2450.4.a.j		1	7.b	odd	2	1
2450.4.a.m		1	1.a	even	1	1	trivial

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} - 1 $

$ T_{11} + 30 $

$ T_{19} + 2 $

$ T_{23} - 183 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 2 $ T + 2
$3$	$ T - 1 $ T - 1
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T + 30 $ T + 30
$13$	$ T - 44 $ T - 44
$17$	$ T + 24 $ T + 24
$19$	$ T + 2 $ T + 2
$23$	$ T - 183 $ T - 183
$29$	$ T + 279 $ T + 279
$31$	$ T - 40 $ T - 40
$37$	$ T - 76 $ T - 76
$41$	$ T - 423 $ T - 423
$43$	$ T + 305 $ T + 305
$47$	$ T - 456 $ T - 456
$53$	$ T - 198 $ T - 198
$59$	$ T - 462 $ T - 462
$61$	$ T + 281 $ T + 281
$67$	$ T - 499 $ T - 499
$71$	$ T + 534 $ T + 534
$73$	$ T - 800 $ T - 800
$79$	$ T + 790 $ T + 790
$83$	$ T + 597 $ T + 597
$89$	$ T + 1017 $ T + 1017
$97$	$ T + 1330 $ T + 1330
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Classical	Maass
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Elliptic curves over $\Q$
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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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