LMFDB - Newform orbit 280.4.a.c

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [280,4,Mod(1,280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(280, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("280.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	280.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,5,0,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.5205348016$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
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 + 5 q^{3} - 5 q^{5} - 7 q^{7} - 2 q^{9} - 39 q^{11} - 19 q^{13} - 25 q^{15} - 37 q^{17} - 18 q^{19} - 35 q^{21} - 90 q^{23} + 25 q^{25} - 145 q^{27} + 99 q^{29} - 32 q^{31} - 195 q^{33} + 35 q^{35} + 46 q^{37}+ \cdots + 78 q^{99}+O(q^{100}) $

q + 5 * q^3 - 5 * q^5 - 7 * q^7 - 2 * q^9 - 39 * q^11 - 19 * q^13 - 25 * q^15 - 37 * q^17 - 18 * q^19 - 35 * q^21 - 90 * q^23 + 25 * q^25 - 145 * q^27 + 99 * q^29 - 32 * q^31 - 195 * q^33 + 35 * q^35 + 46 * q^37 - 95 * q^39 - 248 * q^41 + 178 * q^43 + 10 * q^45 + 429 * q^47 + 49 * q^49 - 185 * q^51 - 652 * q^53 + 195 * q^55 - 90 * q^57 + 40 * q^59 - 36 * q^61 + 14 * q^63 + 95 * q^65 - 348 * q^67 - 450 * q^69 + 72 * q^71 - 1190 * q^73 + 125 * q^75 + 273 * q^77 + 699 * q^79 - 671 * q^81 - 116 * q^83 + 185 * q^85 + 495 * q^87 - 704 * q^89 + 133 * q^91 - 160 * q^93 + 90 * q^95 + 223 * q^97 + 78 * q^99

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

5.00000

−5.00000

−7.00000

−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	280.4.a.c	✓	1
4.b	odd	2	1		560.4.a.e		1
5.b	even	2	1		1400.4.a.d		1
5.c	odd	4	2		1400.4.g.c		2
7.b	odd	2	1		1960.4.a.d		1
8.b	even	2	1		2240.4.a.j		1
8.d	odd	2	1		2240.4.a.be		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
280.4.a.c	✓	1	1.a	even	1	1	trivial
560.4.a.e		1	4.b	odd	2	1
1400.4.a.d		1	5.b	even	2	1
1400.4.g.c		2	5.c	odd	4	2
1960.4.a.d		1	7.b	odd	2	1
2240.4.a.j		1	8.b	even	2	1
2240.4.a.be		1	8.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{3} - 5 $ T3 - 5 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(280))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 5 $ T - 5
$5$	$ T + 5 $ T + 5
$7$	$ T + 7 $ T + 7
$11$	$ T + 39 $ T + 39
$13$	$ T + 19 $ T + 19
$17$	$ T + 37 $ T + 37
$19$	$ T + 18 $ T + 18
$23$	$ T + 90 $ T + 90
$29$	$ T - 99 $ T - 99
$31$	$ T + 32 $ T + 32
$37$	$ T - 46 $ T - 46
$41$	$ T + 248 $ T + 248
$43$	$ T - 178 $ T - 178
$47$	$ T - 429 $ T - 429
$53$	$ T + 652 $ T + 652
$59$	$ T - 40 $ T - 40
$61$	$ T + 36 $ T + 36
$67$	$ T + 348 $ T + 348
$71$	$ T - 72 $ T - 72
$73$	$ T + 1190 $ T + 1190
$79$	$ T - 699 $ T - 699
$83$	$ T + 116 $ T + 116
$89$	$ T + 704 $ T + 704
$97$	$ T - 223 $ T - 223
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Elliptic curves over $\Q$
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Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	280.a (trivial)

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