LMFDB - Newform orbit 1456.4.a.f

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1456,4,Mod(1,1456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1456.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1456, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1456.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,2,0,-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:	$85.9067809684$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
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^{3} - 5 q^{5} + 7 q^{7} - 23 q^{9} + 36 q^{11} - 13 q^{13} - 10 q^{15} + 26 q^{17} + 47 q^{19} + 14 q^{21} + 99 q^{23} - 100 q^{25} - 100 q^{27} - 61 q^{29} + 23 q^{31} + 72 q^{33} - 35 q^{35}+ \cdots - 828 q^{99}+O(q^{100}) $

q + 2 * q^3 - 5 * q^5 + 7 * q^7 - 23 * q^9 + 36 * q^11 - 13 * q^13 - 10 * q^15 + 26 * q^17 + 47 * q^19 + 14 * q^21 + 99 * q^23 - 100 * q^25 - 100 * q^27 - 61 * q^29 + 23 * q^31 + 72 * q^33 - 35 * q^35 - 50 * q^37 - 26 * q^39 + 70 * q^41 + 19 * q^43 + 115 * q^45 - 191 * q^47 + 49 * q^49 + 52 * q^51 + 195 * q^53 - 180 * q^55 + 94 * q^57 - 264 * q^59 + 310 * q^61 - 161 * q^63 + 65 * q^65 + 190 * q^67 + 198 * q^69 + 166 * q^71 + 873 * q^73 - 200 * q^75 + 252 * q^77 + 1191 * q^79 + 421 * q^81 - 259 * q^83 - 130 * q^85 - 122 * q^87 - 635 * q^89 - 91 * q^91 + 46 * q^93 - 235 * q^95 + 133 * q^97 - 828 * 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

2.00000

−5.00000

7.00000

−23.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$7$	$ -1 $
$13$	$ +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	1456.4.a.f		1
4.b	odd	2	1		182.4.a.c	✓	1
12.b	even	2	1		1638.4.a.e		1
28.d	even	2	1		1274.4.a.g		1
52.b	odd	2	1		2366.4.a.b		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
182.4.a.c	✓	1	4.b	odd	2	1
1274.4.a.g		1	28.d	even	2	1
1456.4.a.f		1	1.a	even	1	1	trivial
1638.4.a.e		1	12.b	even	2	1
2366.4.a.b		1	52.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 $S_{4}^{\mathrm{new}}(\Gamma_0(1456))$:

$ T_{3} - 2 $

T3 - 2

$ T_{5} + 5 $

T5 + 5

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 2 $ T - 2
$5$	$ T + 5 $ T + 5
$7$	$ T - 7 $ T - 7
$11$	$ T - 36 $ T - 36
$13$	$ T + 13 $ T + 13
$17$	$ T - 26 $ T - 26
$19$	$ T - 47 $ T - 47
$23$	$ T - 99 $ T - 99
$29$	$ T + 61 $ T + 61
$31$	$ T - 23 $ T - 23
$37$	$ T + 50 $ T + 50
$41$	$ T - 70 $ T - 70
$43$	$ T - 19 $ T - 19
$47$	$ T + 191 $ T + 191
$53$	$ T - 195 $ T - 195
$59$	$ T + 264 $ T + 264
$61$	$ T - 310 $ T - 310
$67$	$ T - 190 $ T - 190
$71$	$ T - 166 $ T - 166
$73$	$ T - 873 $ T - 873
$79$	$ T - 1191 $ T - 1191
$83$	$ T + 259 $ T + 259
$89$	$ T + 635 $ T + 635
$97$	$ T - 133 $ T - 133
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Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1456.a (trivial)

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