LMFDB - Newform orbit 795.1.x.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [795,1,Mod(44,795)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(795, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([13, 13, 4]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("795.44");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 795 = 3 \cdot 5 \cdot 53 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	795.x (of order $26$, degree $12$, minimal)

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:	no
Analytic conductor:	$0.396756685043$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{26})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{13}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{13} - \cdots)$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/795\mathbb{Z}\right)^\times$.

$n$	$266$	$637$	$691$
$\chi(n)$	$-1$	$-1$	$\zeta_{26}^{4}$

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} $

44.1

0.970942	+	0.239316i
−0.885456	+	0.464723i
0.748511	+	0.663123i
−0.885456	−	0.464723i
−0.568065	−	0.822984i
0.748511	−	0.663123i
−0.120537	−	0.992709i
0.970942	−	0.239316i
−0.568065	+	0.822984i
−0.120537	+	0.992709i
0.354605	+	0.935016i
0.354605	−	0.935016i

0.627974

0.329586i

0.354605

−

0.935016i

−0.282340

−

0.409041i

0.748511

0.663123i

0.530851

−

0.470293i

−0.127974

−

1.05396i

−0.748511

−

0.663123i

0.251489

0.663123i

89.1

0.850405

−

1.23202i

0.748511

−

0.663123i

−0.440091

−

1.16042i

−0.120537

0.992709i

−0.180446

−

1.48611i

−0.350405

−

0.0863671i

0.120537

−

0.992709i

1.12054

0.992709i

119.1

−0.213460

−

1.75800i

−0.885456

0.464723i

−2.07406

0.511209i

−0.568065

0.822984i

1.00599

1.45743i

0.713460

1.88124i

0.568065

−

0.822984i

1.56806

0.822984i

134.1

0.850405

1.23202i

0.748511

0.663123i

−0.440091

1.16042i

−0.120537

−

0.992709i

−0.180446

1.48611i

−0.350405

0.0863671i

0.120537

0.992709i

1.12054

−

0.992709i

254.1

0.0854858

−

0.225408i

−0.120537

−

0.992709i

0.705010

0.624584i

0.970942

−

0.239316i

−0.234068

−

0.0576926i

0.414514

−

0.217554i

−0.970942

0.239316i

0.0290582

−

0.239316i

314.1

−0.213460

1.75800i

−0.885456

−

0.464723i

−2.07406

−

0.511209i

−0.568065

−

0.822984i

1.00599

−

1.45743i

0.713460

−

1.88124i

0.568065

0.822984i

1.56806

−

0.822984i

434.1

1.10312

−

0.271894i

−0.568065

0.822984i

0.257482

−

0.135137i

0.354605

0.935016i

−0.402877

1.06230i

−0.603116

0.534314i

−0.354605

−

0.935016i

0.645395

0.935016i

524.1

0.627974

−

0.329586i

0.354605

0.935016i

−0.282340

0.409041i

0.748511

−

0.663123i

0.530851

0.470293i

−0.127974

1.05396i

−0.748511

0.663123i

0.251489

−

0.663123i

554.1

0.0854858

0.225408i

−0.120537

0.992709i

0.705010

−

0.624584i

0.970942

0.239316i

−0.234068

0.0576926i

0.414514

0.217554i

−0.970942

−

0.239316i

0.0290582

0.239316i

599.1

1.10312

0.271894i

−0.568065

−

0.822984i

0.257482

0.135137i

0.354605

−

0.935016i

−0.402877

−

1.06230i

−0.603116

−

0.534314i

−0.354605

0.935016i

0.645395

−

0.935016i

629.1

−1.45352

1.28771i

0.970942

0.239316i

0.333997

−

2.75071i

−0.885456

−

0.464723i

−1.71945

0.902438i

1.95352

2.83016i

0.885456

0.464723i

1.88546

−

0.464723i

704.1

−1.45352

−

1.28771i

0.970942

−

0.239316i

0.333997

2.75071i

−0.885456

0.464723i

−1.71945

−

0.902438i

1.95352

−

2.83016i

0.885456

−

0.464723i

1.88546

0.464723i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
15.d	odd	2	1	CM by $\Q(\sqrt{-15}) $
53.d	even	13	1	inner
795.x	odd	26	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	795.1.x.b	yes	12
3.b	odd	2	1		795.1.x.a	✓	12
5.b	even	2	1		795.1.x.a	✓	12
5.c	odd	4	2		3975.1.bt.a		24
15.d	odd	2	1	CM	795.1.x.b	yes	12
15.e	even	4	2		3975.1.bt.a		24
53.d	even	13	1	inner	795.1.x.b	yes	12
159.j	odd	26	1		795.1.x.a	✓	12
265.n	even	26	1		795.1.x.a	✓	12
265.q	odd	52	2		3975.1.bt.a		24
795.x	odd	26	1	inner	795.1.x.b	yes	12
795.bi	even	52	2		3975.1.bt.a		24

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
795.1.x.a	✓	12	3.b	odd	2	1
795.1.x.a	✓	12	5.b	even	2	1
795.1.x.a	✓	12	159.j	odd	26	1
795.1.x.a	✓	12	265.n	even	26	1
795.1.x.b	yes	12	1.a	even	1	1	trivial
795.1.x.b	yes	12	15.d	odd	2	1	CM
795.1.x.b	yes	12	53.d	even	13	1	inner
795.1.x.b	yes	12	795.x	odd	26	1	inner
3975.1.bt.a		24	5.c	odd	4	2
3975.1.bt.a		24	15.e	even	4	2
3975.1.bt.a		24	265.q	odd	52	2
3975.1.bt.a		24	795.bi	even	52	2

This newform subspace can be constructed as the kernel of the linear operator $ T_{2}^{12} - 2 T_{2}^{11} + 4 T_{2}^{10} - 8 T_{2}^{9} + 16 T_{2}^{8} - 32 T_{2}^{7} + 64 T_{2}^{6} + \cdots + 1 $ T2^12 - 2*T2^11 + 4*T2^10 - 8*T2^9 + 16*T2^8 - 32*T2^7 + 64*T2^6 - 115*T2^5 + 139*T2^4 - 96*T2^3 + 36*T2^2 - 7*T2 + 1 acting on $S_{1}^{\mathrm{new}}(795, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T^{12} - 2 T^{11} + \cdots + 1 $ T^12 - 2T^11 + 4T^10 - 8T^9 + 16T^8 - 32T^7 + 64T^6 - 115T^5 + 139T^4 - 96T^3 + 36T^2 - 7*T + 1
$3$	$ T^{12} - T^{11} + \cdots + 1 $ T^12 - T^11 + T^10 - T^9 + T^8 - T^7 + T^6 - T^5 + T^4 - T^3 + T^2 - T + 1
$5$	$ T^{12} - T^{11} + \cdots + 1 $ T^12 - T^11 + T^10 - T^9 + T^8 - T^7 + T^6 - T^5 + T^4 - T^3 + T^2 - T + 1
$7$	$ T^{12} $ T^12
$11$	$ T^{12} $ T^12
$13$	$ T^{12} $ T^12
$17$	$ T^{12} - 2 T^{11} + \cdots + 1 $ T^12 - 2T^11 + 4T^10 + 5T^9 - 10T^8 + 20T^7 + 12T^6 - 24T^5 + 35T^4 - 5T^3 + 10T^2 + 6*T + 1
$19$	$ T^{12} + 2 T^{11} + \cdots + 1 $ T^12 + 2T^11 + 4T^10 - 5T^9 - 10T^8 - 20T^7 + 12T^6 + 24T^5 + 35T^4 + 5T^3 + 10T^2 - 6*T + 1
$23$	$ (T^{6} - T^{5} - 5 T^{4} + \cdots - 1)^{2} $ (T^6 - T^5 - 5T^4 + 4T^3 + 6T^2 - 3T - 1)^2
$29$	$ T^{12} $ T^12
$31$	$ T^{12} + 2 T^{11} + \cdots + 1 $ T^12 + 2T^11 + 4T^10 + 8T^9 + 3T^8 + 6T^7 + 12T^6 - 15T^5 + 9T^4 + 18T^3 + 23T^2 + 7*T + 1
$37$	$ T^{12} $ T^12
$41$	$ T^{12} $ T^12
$43$	$ T^{12} $ T^12
$47$	$ T^{12} - 2 T^{11} + \cdots + 1 $ T^12 - 2T^11 + 4T^10 + 5T^9 - 10T^8 + 20T^7 + 12T^6 - 24T^5 + 35T^4 - 5T^3 + 10T^2 + 6*T + 1
$53$	$ T^{12} - T^{11} + \cdots + 1 $ T^12 - T^11 + T^10 - T^9 + T^8 - T^7 + T^6 - T^5 + T^4 - T^3 + T^2 - T + 1
$59$	$ T^{12} $ T^12
$61$	$ T^{12} - 11 T^{11} + \cdots + 1 $ T^12 - 11T^11 + 56T^10 - 174T^9 + 367T^8 - 553T^7 + 610T^6 - 496T^5 + 295T^4 - 125T^3 + 36T^2 - 6*T + 1
$67$	$ T^{12} $ T^12
$71$	$ T^{12} $ T^12
$73$	$ T^{12} $ T^12
$79$	$ T^{12} + 2 T^{11} + \cdots + 1 $ T^12 + 2T^11 + 4T^10 + 8T^9 + 16T^8 + 6T^7 - T^6 - 2T^5 - 4T^4 - 21T^3 + 23T^2 - 6T + 1
$83$	$ (T^{6} - T^{5} - 5 T^{4} + \cdots - 1)^{2} $ (T^6 - T^5 - 5T^4 + 4T^3 + 6T^2 - 3T - 1)^2
$89$	$ T^{12} $ T^12
$97$	$ T^{12} $ T^12
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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 795 = 3 \cdot 5 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	795.x (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\( q + ( - \zeta_{26}^{10} + \zeta_{26}^{7}) q^{2} - \zeta_{26}^{8} q^{3} + ( - \zeta_{26}^{7} + \zeta_{26}^{4} - \zeta_{26}) q^{4} + \zeta_{26}^{3} q^{5} + ( - \zeta_{26}^{5} + \zeta_{26}^{2}) q^{6} + (\zeta_{26}^{11} - \zeta_{26}^{8} + \cdots - \zeta_{26}) q^{8} + \cdots - \zeta_{26}^{3} q^{9} +O(q^{10}) \) q + (-z^10 + z^7) * q^2 - z^8 * q^3 + (-z^7 + z^4 - z) * q^4 + z^3 * q^5 + (-z^5 + z^2) * q^6 + (z^11 - z^8 - z^4 - z) * q^8 - z^3 * q^9	\( q + ( - \zeta_{26}^{10} + \zeta_{26}^{7}) q^{2} - \zeta_{26}^{8} q^{3} + ( - \zeta_{26}^{7} + \zeta_{26}^{4} - \zeta_{26}) q^{4} + \zeta_{26}^{3} q^{5} + ( - \zeta_{26}^{5} + \zeta_{26}^{2}) q^{6} + (\zeta_{26}^{11} - \zeta_{26}^{8} + \cdots - \zeta_{26}) q^{8} + \cdots + (\zeta_{26}^{11} + \zeta_{26}) q^{98} +O(q^{100}) \) q + (-z^10 + z^7) * q^2 - z^8 * q^3 + (-z^7 + z^4 - z) * q^4 + z^3 * q^5 + (-z^5 + z^2) * q^6 + (z^11 - z^8 - z^4 - z) * q^8 - z^3 * q^9 + (z^10 + 1) * q^10 + (-z^12 + z^9 - z^2) * q^12 - z^11 * q^15 + (-z^11 + z^8 - z^5 + z^2 - z) * q^16 + (-z^12 - z^2) * q^17 + (-z^10 - 1) * q^18 + (z^10 + z^8) * q^19 + (-z^10 + z^7 - z^4) * q^20 + (-z^12 + z) * q^23 + (z^12 - z^9 + z^6 - z^3) * q^24 + z^6 * q^25 + z^11 * q^27 + (-z^8 + z^5) * q^30 + (z^12 - z^3) * q^31 + (-z^12 + z^11 + z^9 - z^8 + z^5 + z^2) * q^32 + (z^12 - z^9 + z^6) * q^34 + (z^10 - z^7 + z^4) * q^36 + (z^7 + z^5 - z^4 - z^2) * q^38 + (-z^11 - z^7 + z^4 - z) * q^40 - z^6 * q^45 + (-z^11 - z^9 + z^8 + z^6) * q^46 + (-z^6 + z) * q^47 + (-z^10 + z^9 - z^6 + z^3 - 1) * q^48 + z^4 * q^49 + (z^3 - 1) * q^50 + (z^10 - z^7) * q^51 + z^7 * q^53 + (z^8 - z^5) * q^54 + (z^5 + z^3) * q^57 + (z^12 - z^5 + z^2) * q^60 + (z^12 + 1) * q^61 + (-z^10 + z^9 - z^6 - 1) * q^62 + (z^12 - z^9 + z^8 + z^6 - z^5 - z^3 - z^2) * q^64 + (z^9 - z^6 + z^3 - 1) * q^68 + (-z^9 - z^7) * q^69 + (z^11 + z^7 - z^4 + z) * q^72 + z * q^75 + (z^12 - z^11 - z^9 + z^4 + z^2 - z) * q^76 + (z^8 - z) * q^79 + (z^11 - z^8 + z^5 - z^4 + z) * q^80 + z^6 * q^81 + (z^9 - z^4) * q^83 + (-z^5 + z^2) * q^85 + (-z^3 + 1) * q^90 + (-z^8 - z^6 + z^5 + z^3 - z^2 - 1) * q^92 + (z^11 + z^7) * q^93 + (-z^11 + z^8 - z^3 + 1) * q^94 + (z^11 - 1) * q^95 + (z^10 - z^7 + z^6 + z^4 - z^3 + 1) * q^96 + (z^11 + z) * q^98
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + q^{3} - 3 q^{4} + q^{5} - 2 q^{6} + 4 q^{8} - q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + q^3 - 3 * q^4 + q^5 - 2 * q^6 + 4 * q^8 - q^9	\( 12 q + 2 q^{2} + q^{3} - 3 q^{4} + q^{5} - 2 q^{6} + 4 q^{8} - q^{9} + 11 q^{10} + 3 q^{12} - q^{15} - 5 q^{16} + 2 q^{17} - 11 q^{18} - 2 q^{19} + 3 q^{20} + 2 q^{23} - 4 q^{24} - q^{25} + q^{27} + 2 q^{30} - 2 q^{31} + 6 q^{32} - 4 q^{34} - 3 q^{36} + 4 q^{38} - 4 q^{40} + q^{45} - 4 q^{46} + 2 q^{47} - 8 q^{48} - q^{49} - 11 q^{50} - 2 q^{51} + q^{53} - 2 q^{54} + 2 q^{57} - 3 q^{60} + 11 q^{61} - 9 q^{62} - 7 q^{64} - 7 q^{68} - 2 q^{69} + 4 q^{72} + q^{75} - 6 q^{76} - 2 q^{79} + 5 q^{80} - q^{81} + 2 q^{83} - 2 q^{85} + 11 q^{90} - 7 q^{92} + 2 q^{93} + 9 q^{94} - 11 q^{95} + 7 q^{96} + 2 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 + q^3 - 3 * q^4 + q^5 - 2 * q^6 + 4 * q^8 - q^9 + 11 * q^10 + 3 * q^12 - q^15 - 5 * q^16 + 2 * q^17 - 11 * q^18 - 2 * q^19 + 3 * q^20 + 2 * q^23 - 4 * q^24 - q^25 + q^27 + 2 * q^30 - 2 * q^31 + 6 * q^32 - 4 * q^34 - 3 * q^36 + 4 * q^38 - 4 * q^40 + q^45 - 4 * q^46 + 2 * q^47 - 8 * q^48 - q^49 - 11 * q^50 - 2 * q^51 + q^53 - 2 * q^54 + 2 * q^57 - 3 * q^60 + 11 * q^61 - 9 * q^62 - 7 * q^64 - 7 * q^68 - 2 * q^69 + 4 * q^72 + q^75 - 6 * q^76 - 2 * q^79 + 5 * q^80 - q^81 + 2 * q^83 - 2 * q^85 + 11 * q^90 - 7 * q^92 + 2 * q^93 + 9 * q^94 - 11 * q^95 + 7 * q^96 + 2 * q^98

Introduction

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Newspace parameters

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Hecke kernels

Hecke characteristic polynomials

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	795.1.x.b

Level	$795$
Weight	$1$
Character orbit	795.x
Analytic conductor	$0.397$
Analytic rank	$0$
Dimension	$12$
Projective image	$D_{13}$
CM discriminant	-15
Inner twists	$4$

Self dual:	no
Analytic conductor:	\(0.396756685043\)
Analytic rank:	\(0\)
Dimension:	\(12\)
Coefficient field:	\(\Q(\zeta_{26})\)
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	\( x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Projective image:	\(D_{13}\)
Projective field:	Galois closure of \(\mathbb{Q}[x]/(x^{13} - \cdots)\)

\(n\)	\(266\)	\(637\)	\(691\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(\zeta_{26}^{4}\)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 44.1
Significant digits:
Format:

$p$	$F_p(T)$
$2$	\( T^{12} - 2 T^{11} + \cdots + 1 \) T^12 - 2T^11 + 4T^10 - 8T^9 + 16T^8 - 32T^7 + 64T^6 - 115T^5 + 139T^4 - 96T^3 + 36T^2 - 7*T + 1
$3$	\( T^{12} - T^{11} + \cdots + 1 \) T^12 - T^11 + T^10 - T^9 + T^8 - T^7 + T^6 - T^5 + T^4 - T^3 + T^2 - T + 1
$5$	\( T^{12} - T^{11} + \cdots + 1 \) T^12 - T^11 + T^10 - T^9 + T^8 - T^7 + T^6 - T^5 + T^4 - T^3 + T^2 - T + 1
$7$	\( T^{12} \) T^12
$11$	\( T^{12} \) T^12
$13$	\( T^{12} \) T^12
$17$	\( T^{12} - 2 T^{11} + \cdots + 1 \) T^12 - 2T^11 + 4T^10 + 5T^9 - 10T^8 + 20T^7 + 12T^6 - 24T^5 + 35T^4 - 5T^3 + 10T^2 + 6*T + 1
$19$	\( T^{12} + 2 T^{11} + \cdots + 1 \) T^12 + 2T^11 + 4T^10 - 5T^9 - 10T^8 - 20T^7 + 12T^6 + 24T^5 + 35T^4 + 5T^3 + 10T^2 - 6*T + 1
$23$	\( (T^{6} - T^{5} - 5 T^{4} + \cdots - 1)^{2} \) (T^6 - T^5 - 5T^4 + 4T^3 + 6T^2 - 3T - 1)^2
$29$	\( T^{12} \) T^12
$31$	\( T^{12} + 2 T^{11} + \cdots + 1 \) T^12 + 2T^11 + 4T^10 + 8T^9 + 3T^8 + 6T^7 + 12T^6 - 15T^5 + 9T^4 + 18T^3 + 23T^2 + 7*T + 1
$37$	\( T^{12} \) T^12
$41$	\( T^{12} \) T^12
$43$	\( T^{12} \) T^12
$47$	\( T^{12} - 2 T^{11} + \cdots + 1 \) T^12 - 2T^11 + 4T^10 + 5T^9 - 10T^8 + 20T^7 + 12T^6 - 24T^5 + 35T^4 - 5T^3 + 10T^2 + 6*T + 1
$53$	\( T^{12} - T^{11} + \cdots + 1 \) T^12 - T^11 + T^10 - T^9 + T^8 - T^7 + T^6 - T^5 + T^4 - T^3 + T^2 - T + 1
$59$	\( T^{12} \) T^12
$61$	\( T^{12} - 11 T^{11} + \cdots + 1 \) T^12 - 11T^11 + 56T^10 - 174T^9 + 367T^8 - 553T^7 + 610T^6 - 496T^5 + 295T^4 - 125T^3 + 36T^2 - 6*T + 1
$67$	\( T^{12} \) T^12
$71$	\( T^{12} \) T^12
$73$	\( T^{12} \) T^12
$79$	\( T^{12} + 2 T^{11} + \cdots + 1 \) T^12 + 2T^11 + 4T^10 + 8T^9 + 16T^8 + 6T^7 - T^6 - 2T^5 - 4T^4 - 21T^3 + 23T^2 - 6T + 1
$83$	\( (T^{6} - T^{5} - 5 T^{4} + \cdots - 1)^{2} \) (T^6 - T^5 - 5T^4 + 4T^3 + 6T^2 - 3T - 1)^2
$89$	\( T^{12} \) T^12
$97$	\( T^{12} \) T^12
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