LMFDB - Newform orbit 855.4.a.a

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,4,Mod(1,855)] 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("855.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	855.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-5,0,17,-5,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$50.4466330549$
Analytic rank:	$2$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
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^{2} + 17 q^{4} - 5 q^{5} - 32 q^{7} - 45 q^{8} + 25 q^{10} + 12 q^{11} - 42 q^{13} + 160 q^{14} + 89 q^{16} - 114 q^{17} + 19 q^{19} - 85 q^{20} - 60 q^{22} - 160 q^{23} + 25 q^{25} + 210 q^{26}+ \cdots - 3405 q^{98}+O(q^{100}) $

q - 5 * q^2 + 17 * q^4 - 5 * q^5 - 32 * q^7 - 45 * q^8 + 25 * q^10 + 12 * q^11 - 42 * q^13 + 160 * q^14 + 89 * q^16 - 114 * q^17 + 19 * q^19 - 85 * q^20 - 60 * q^22 - 160 * q^23 + 25 * q^25 + 210 * q^26 - 544 * q^28 - 214 * q^29 - 144 * q^31 - 85 * q^32 + 570 * q^34 + 160 * q^35 + 94 * q^37 - 95 * q^38 + 225 * q^40 + 6 * q^41 - 308 * q^43 + 204 * q^44 + 800 * q^46 - 184 * q^47 + 681 * q^49 - 125 * q^50 - 714 * q^52 + 274 * q^53 - 60 * q^55 + 1440 * q^56 + 1070 * q^58 - 276 * q^59 - 826 * q^61 + 720 * q^62 - 287 * q^64 + 210 * q^65 + 52 * q^67 - 1938 * q^68 - 800 * q^70 + 344 * q^71 - 166 * q^73 - 470 * q^74 + 323 * q^76 - 384 * q^77 - 688 * q^79 - 445 * q^80 - 30 * q^82 - 996 * q^83 + 570 * q^85 + 1540 * q^86 - 540 * q^88 - 1578 * q^89 + 1344 * q^91 - 2720 * q^92 + 920 * q^94 - 95 * q^95 + 786 * q^97 - 3405 * q^98

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

17.0000

−5.00000

−32.0000

−45.0000

25.0000

Atkin-Lehner signs

$ p $	Sign
$3$	$ -1 $
$5$	$ +1 $
$19$	$ -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	855.4.a.a		1
3.b	odd	2	1		95.4.a.d	✓	1
12.b	even	2	1		1520.4.a.c		1
15.d	odd	2	1		475.4.a.a		1
15.e	even	4	2		475.4.b.a		2
57.d	even	2	1		1805.4.a.a		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.4.a.d	✓	1	3.b	odd	2	1
475.4.a.a		1	15.d	odd	2	1
475.4.b.a		2	15.e	even	4	2
855.4.a.a		1	1.a	even	1	1	trivial
1520.4.a.c		1	12.b	even	2	1
1805.4.a.a		1	57.d	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(855))$:

$ T_{2} + 5 $

T2 + 5

$ T_{7} + 32 $

T7 + 32

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 5 $ T + 5
$3$	$ T $ T
$5$	$ T + 5 $ T + 5
$7$	$ T + 32 $ T + 32
$11$	$ T - 12 $ T - 12
$13$	$ T + 42 $ T + 42
$17$	$ T + 114 $ T + 114
$19$	$ T - 19 $ T - 19
$23$	$ T + 160 $ T + 160
$29$	$ T + 214 $ T + 214
$31$	$ T + 144 $ T + 144
$37$	$ T - 94 $ T - 94
$41$	$ T - 6 $ T - 6
$43$	$ T + 308 $ T + 308
$47$	$ T + 184 $ T + 184
$53$	$ T - 274 $ T - 274
$59$	$ T + 276 $ T + 276
$61$	$ T + 826 $ T + 826
$67$	$ T - 52 $ T - 52
$71$	$ T - 344 $ T - 344
$73$	$ T + 166 $ T + 166
$79$	$ T + 688 $ T + 688
$83$	$ T + 996 $ T + 996
$89$	$ T + 1578 $ T + 1578
$97$	$ T - 786 $ T - 786
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Overview	Random
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Classical	Maass
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Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	855.a (trivial)

\(n\):		e.g. 2-40 or 80-90
Significant digits:
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