LMFDB - Newform orbit 2240.4.a.v

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,4,Mod(1,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("2240.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2240.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:	$132.164278413$
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 + q^{3} + 5 q^{5} + 7 q^{7} - 26 q^{9}+O(q^{10}) $

$ q + q^{3} + 5 q^{5} + 7 q^{7} - 26 q^{9} + 65 q^{11} - 13 q^{13} + 5 q^{15} - 73 q^{17} + 142 q^{19} + 7 q^{21} + 130 q^{23} + 25 q^{25} - 53 q^{27} - 111 q^{29} + 256 q^{31} + 65 q^{33} + 35 q^{35} + 266 q^{37} - 13 q^{39} - 424 q^{41} - 534 q^{43} - 130 q^{45} - 269 q^{47} + 49 q^{49} - 73 q^{51} + 132 q^{53} + 325 q^{55} + 142 q^{57} + 224 q^{59} + 572 q^{61} - 182 q^{63} - 65 q^{65} + 108 q^{67} + 130 q^{69} + 560 q^{71} + 586 q^{73} + 25 q^{75} + 455 q^{77} + 57 q^{79} + 649 q^{81} - 252 q^{83} - 365 q^{85} - 111 q^{87} - 184 q^{89} - 91 q^{91} + 256 q^{93} + 710 q^{95} - 605 q^{97} - 1690 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

1.00000

5.00000

7.00000

−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	2240.4.a.v		1
4.b	odd	2	1		2240.4.a.r		1
8.b	even	2	1		70.4.a.c	✓	1
8.d	odd	2	1		560.4.a.i		1
24.h	odd	2	1		630.4.a.x		1
40.f	even	2	1		350.4.a.r		1
40.i	odd	4	2		350.4.c.h		2
56.h	odd	2	1		490.4.a.d		1
56.j	odd	6	2		490.4.e.n		2
56.p	even	6	2		490.4.e.o		2
280.c	odd	2	1		2450.4.a.bc		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.4.a.c	✓	1	8.b	even	2	1
350.4.a.r		1	40.f	even	2	1
350.4.c.h		2	40.i	odd	4	2
490.4.a.d		1	56.h	odd	2	1
490.4.e.n		2	56.j	odd	6	2
490.4.e.o		2	56.p	even	6	2
560.4.a.i		1	8.d	odd	2	1
630.4.a.x		1	24.h	odd	2	1
2240.4.a.r		1	4.b	odd	2	1
2240.4.a.v		1	1.a	even	1	1	trivial
2450.4.a.bc		1	280.c	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(2240))$:

$ T_{3} - 1 $

$ T_{11} - 65 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 1 $ T - 1
$5$	$ T - 5 $ T - 5
$7$	$ T - 7 $ T - 7
$11$	$ T - 65 $ T - 65
$13$	$ T + 13 $ T + 13
$17$	$ T + 73 $ T + 73
$19$	$ T - 142 $ T - 142
$23$	$ T - 130 $ T - 130
$29$	$ T + 111 $ T + 111
$31$	$ T - 256 $ T - 256
$37$	$ T - 266 $ T - 266
$41$	$ T + 424 $ T + 424
$43$	$ T + 534 $ T + 534
$47$	$ T + 269 $ T + 269
$53$	$ T - 132 $ T - 132
$59$	$ T - 224 $ T - 224
$61$	$ T - 572 $ T - 572
$67$	$ T - 108 $ T - 108
$71$	$ T - 560 $ T - 560
$73$	$ T - 586 $ T - 586
$79$	$ T - 57 $ T - 57
$83$	$ T + 252 $ T + 252
$89$	$ T + 184 $ T + 184
$97$	$ T + 605 $ T + 605
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Elliptic curves over $\Q$
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Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2240.a (trivial)

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