LMFDB - Newform orbit 3800.1.cv.d

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3800,1,Mod(251,3800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3800, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 0, 2]))

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

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

chi := DirichletCharacter("3800.251");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3800 = 2^{3} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3800.cv (of order $18$, degree $6$, 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:	$1.89644704801$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{9}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{9} - \cdots)$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times$.

$n$	$401$	$951$	$1901$	$1977$
$\chi(n)$	$-\zeta_{18}$	$-1$	$-1$	$1$

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} $

251.1

−0.766044	−	0.642788i
−0.766044	+	0.642788i
−0.173648	+	0.984808i
−0.173648	−	0.984808i
0.939693	+	0.342020i
0.939693	−	0.342020i

0.939693

0.342020i

−0.266044

−

1.50881i

0.766044

0.642788i

0.266044

−

1.50881i

0.500000

0.866025i

−1.26604

0.460802i

651.1

0.939693

−

0.342020i

−0.266044

1.50881i

0.766044

−

0.642788i

0.266044

1.50881i

0.500000

−

0.866025i

−1.26604

−

0.460802i

1051.1

−0.766044

0.642788i

0.326352

0.118782i

0.173648

−

0.984808i

−0.326352

0.118782i

0.500000

0.866025i

−0.673648

−

0.565258i

1251.1

−0.766044

−

0.642788i

0.326352

−

0.118782i

0.173648

0.984808i

−0.326352

−

0.118782i

0.500000

−

0.866025i

−0.673648

0.565258i

1651.1

−0.173648

0.984808i

1.43969

1.20805i

−0.939693

−

0.342020i

−1.43969

1.20805i

0.500000

−

0.866025i

0.439693

2.49362i

2251.1

−0.173648

−

0.984808i

1.43969

−

1.20805i

−0.939693

0.342020i

−1.43969

−

1.20805i

0.500000

0.866025i

0.439693

−

2.49362i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.d	odd	2	1	CM by $\Q(\sqrt{-2}) $
19.e	even	9	1	inner
152.u	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3800.1.cv.d	yes	6
5.b	even	2	1		3800.1.cv.b	✓	6
5.c	odd	4	2		3800.1.cq.a		12
8.d	odd	2	1	CM	3800.1.cv.d	yes	6
19.e	even	9	1	inner	3800.1.cv.d	yes	6
40.e	odd	2	1		3800.1.cv.b	✓	6
40.k	even	4	2		3800.1.cq.a		12
95.p	even	18	1		3800.1.cv.b	✓	6
95.q	odd	36	2		3800.1.cq.a		12
152.u	odd	18	1	inner	3800.1.cv.d	yes	6
760.bz	odd	18	1		3800.1.cv.b	✓	6
760.cp	even	36	2		3800.1.cq.a		12

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3800.1.cq.a		12	5.c	odd	4	2
3800.1.cq.a		12	40.k	even	4	2
3800.1.cq.a		12	95.q	odd	36	2
3800.1.cq.a		12	760.cp	even	36	2
3800.1.cv.b	✓	6	5.b	even	2	1
3800.1.cv.b	✓	6	40.e	odd	2	1
3800.1.cv.b	✓	6	95.p	even	18	1
3800.1.cv.b	✓	6	760.bz	odd	18	1
3800.1.cv.d	yes	6	1.a	even	1	1	trivial
3800.1.cv.d	yes	6	8.d	odd	2	1	CM
3800.1.cv.d	yes	6	19.e	even	9	1	inner
3800.1.cv.d	yes	6	152.u	odd	18	1	inner

This newform subspace can be constructed as the kernel of the linear operator $ T_{3}^{6} - 3T_{3}^{5} + 6T_{3}^{4} - 8T_{3}^{3} + 12T_{3}^{2} - 6T_{3} + 1 $ T3^6 - 3*T3^5 + 6*T3^4 - 8*T3^3 + 12*T3^2 - 6*T3 + 1 acting on $S_{1}^{\mathrm{new}}(3800, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T^{6} - T^{3} + 1 $ T^6 - T^3 + 1
$3$	$ T^{6} - 3 T^{5} + \cdots + 1 $ T^6 - 3T^5 + 6T^4 - 8T^3 + 12T^2 - 6*T + 1
$5$	$ T^{6} $ T^6
$7$	$ T^{6} $ T^6
$11$	$ T^{6} + 3 T^{4} + \cdots + 1 $ T^6 + 3T^4 + 2T^3 + 9T^2 + 3T + 1
$13$	$ T^{6} $ T^6
$17$	$ T^{6} - 8T^{3} + 64 $ T^6 - 8*T^3 + 64
$19$	$ T^{6} + T^{3} + 1 $ T^6 + T^3 + 1
$23$	$ T^{6} $ T^6
$29$	$ T^{6} $ T^6
$31$	$ T^{6} $ T^6
$37$	$ T^{6} $ T^6
$41$	$ T^{6} + 3 T^{5} + \cdots + 1 $ T^6 + 3T^5 + 6T^4 + 8T^3 + 3T^2 - 3*T + 1
$43$	$ T^{6} + T^{3} + 1 $ T^6 + T^3 + 1
$47$	$ T^{6} $ T^6
$53$	$ T^{6} $ T^6
$59$	$ T^{6} + 3 T^{5} + \cdots + 1 $ T^6 + 3T^5 + 6T^4 + 8T^3 + 12T^2 + 6*T + 1
$61$	$ T^{6} $ T^6
$67$	$ T^{6} + 6 T^{5} + \cdots + 1 $ T^6 + 6T^5 + 15T^4 + 19T^3 + 12T^2 + 3*T + 1
$71$	$ T^{6} $ T^6
$73$	$ T^{6} - 3 T^{5} + \cdots + 1 $ T^6 - 3T^5 + 6T^4 - 8T^3 + 3T^2 + 3*T + 1
$79$	$ T^{6} $ T^6
$83$	$ T^{6} + 3 T^{4} + \cdots + 1 $ T^6 + 3T^4 - 2T^3 + 9T^2 - 3T + 1
$89$	$ T^{6} - T^{3} + 1 $ T^6 - T^3 + 1
$97$	$ T^{6} - 3 T^{5} + \cdots + 1 $ T^6 - 3T^5 + 6T^4 - 8T^3 + 3T^2 + 3*T + 1
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Overview	Random
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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:	\( N \)	\(=\)	\( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3800.cv (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\( q + \zeta_{18}^{5} q^{2} + (\zeta_{18}^{3} + \zeta_{18}) q^{3} - \zeta_{18} q^{4} + (\zeta_{18}^{8} + \zeta_{18}^{6}) q^{6} - \zeta_{18}^{6} q^{8} + (\zeta_{18}^{6} + \cdots + \zeta_{18}^{2}) q^{9} +O(q^{10}) \) q + z^5 * q^2 + (z^3 + z) * q^3 - z * q^4 + (z^8 + z^6) * q^6 - z^6 * q^8 + (z^6 + z^4 + z^2) * q^9	\( q + \zeta_{18}^{5} q^{2} + (\zeta_{18}^{3} + \zeta_{18}) q^{3} - \zeta_{18} q^{4} + (\zeta_{18}^{8} + \zeta_{18}^{6}) q^{6} - \zeta_{18}^{6} q^{8} + (\zeta_{18}^{6} + \cdots + \zeta_{18}^{2}) q^{9} + \cdots + ( - \zeta_{18}^{7} + \zeta_{18}^{4} + \cdots + 2) q^{99} +O(q^{100}) \) q + z^5 * q^2 + (z^3 + z) * q^3 - z * q^4 + (z^8 + z^6) * q^6 - z^6 * q^8 + (z^6 + z^4 + z^2) * q^9 + (-z^7 - z^5) * q^11 + (-z^4 - z^2) * q^12 + z^2 * q^16 + z^5 * q^17 + (z^7 - z^2 - 1) * q^18 - z^7 * q^19 + (z^3 + z) * q^22 + (-z^7 + 1) * q^24 + (z^7 + z^5 + z^3 - 1) * q^27 + z^7 * q^32 + (-2z^8 - z^6 + z) q^33 - 2z q^34 + (-z^7 - z^5 - z^3) * q^36 + z^3 * q^38 + (-z^7 + z^6) * q^41 + z^8 * q^43 + (z^8 + z^6) * q^44 + (z^5 + z^3) * q^48 + z^6 * q^49 + (2z^8 + 2z^6) * q^51 + (z^8 - z^5 - z^3 - z) * q^54 + (-z^8 + z) * q^57 + (-z^7 - z^3) * q^59 - z^3 * q^64 + (z^6 + 2z^4 + z^2) q^66 + (-z^8 - 1) * q^67 - 2z^6 q^68 + (-z^8 + z^3 + z) * q^72 + (z^7 - z^6) * q^73 + z^8 * q^76 + (z^8 + z^6 + z^4 - z^3 + z) * q^81 + (z^3 - z^2) * q^82 + (z^5 + z) * q^83 - z^4 * q^86 + (-z^4 - z^2) * q^88 + z^7 * q^89 + (z^8 - z) * q^96 + (-z^6 - z^4) * q^97 - z^2 * q^98 + (-z^7 + z^4 + 2z^2 + 2) q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 3 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 3 * q^6 + 3 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 3 q^{6} + 3 q^{8} - 3 q^{9} - 6 q^{18} + 3 q^{22} + 6 q^{24} - 3 q^{27} + 3 q^{33} - 3 q^{36} + 3 q^{38} - 3 q^{41} - 3 q^{44} + 3 q^{48} - 3 q^{49} - 6 q^{51} - 3 q^{54} - 3 q^{59} - 3 q^{64} - 3 q^{66} - 6 q^{67} + 6 q^{68} + 3 q^{72} + 3 q^{73} - 6 q^{81} + 3 q^{82} + 3 q^{97} + 12 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 3 * q^6 + 3 * q^8 - 3 * q^9 - 6 * q^18 + 3 * q^22 + 6 * q^24 - 3 * q^27 + 3 * q^33 - 3 * q^36 + 3 * q^38 - 3 * q^41 - 3 * q^44 + 3 * q^48 - 3 * q^49 - 6 * q^51 - 3 * q^54 - 3 * q^59 - 3 * q^64 - 3 * q^66 - 6 * q^67 + 6 * q^68 + 3 * q^72 + 3 * q^73 - 6 * q^81 + 3 * q^82 + 3 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

$q$-expansion

Character values

Embeddings

Inner twists

Twists

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	3800.1.cv.d

Level	$3800$
Weight	$1$
Character orbit	3800.cv
Analytic conductor	$1.896$
Analytic rank	$0$
Dimension	$6$
Projective image	$D_{9}$
CM discriminant	-8
Inner twists	$4$

Self dual:	no
Analytic conductor:	\(1.89644704801\)
Analytic rank:	\(0\)
Dimension:	\(6\)
Coefficient field:	\(\Q(\zeta_{18})\)
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	\( x^{6} - x^{3} + 1 \) x^6 - x^3 + 1
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Projective image:	\(D_{9}\)
Projective field:	Galois closure of \(\mathbb{Q}[x]/(x^{9} - \cdots)\)

\(n\)	\(401\)	\(951\)	\(1901\)	\(1977\)
\(\chi(n)\)	\(-\zeta_{18}\)	\(-1\)	\(-1\)	\(1\)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 251.1
Significant digits:
Format:

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.d	odd	2	1	CM by \(\Q(\sqrt{-2}) \)
19.e	even	9	1	inner
152.u	odd	18	1	inner

$p$	$F_p(T)$
$2$	\( T^{6} - T^{3} + 1 \) T^6 - T^3 + 1
$3$	\( T^{6} - 3 T^{5} + \cdots + 1 \) T^6 - 3T^5 + 6T^4 - 8T^3 + 12T^2 - 6*T + 1
$5$	\( T^{6} \) T^6
$7$	\( T^{6} \) T^6
$11$	\( T^{6} + 3 T^{4} + \cdots + 1 \) T^6 + 3T^4 + 2T^3 + 9T^2 + 3T + 1
$13$	\( T^{6} \) T^6
$17$	\( T^{6} - 8T^{3} + 64 \) T^6 - 8*T^3 + 64
$19$	\( T^{6} + T^{3} + 1 \) T^6 + T^3 + 1
$23$	\( T^{6} \) T^6
$29$	\( T^{6} \) T^6
$31$	\( T^{6} \) T^6
$37$	\( T^{6} \) T^6
$41$	\( T^{6} + 3 T^{5} + \cdots + 1 \) T^6 + 3T^5 + 6T^4 + 8T^3 + 3T^2 - 3*T + 1
$43$	\( T^{6} + T^{3} + 1 \) T^6 + T^3 + 1
$47$	\( T^{6} \) T^6
$53$	\( T^{6} \) T^6
$59$	\( T^{6} + 3 T^{5} + \cdots + 1 \) T^6 + 3T^5 + 6T^4 + 8T^3 + 12T^2 + 6*T + 1
$61$	\( T^{6} \) T^6
$67$	\( T^{6} + 6 T^{5} + \cdots + 1 \) T^6 + 6T^5 + 15T^4 + 19T^3 + 12T^2 + 3*T + 1
$71$	\( T^{6} \) T^6
$73$	\( T^{6} - 3 T^{5} + \cdots + 1 \) T^6 - 3T^5 + 6T^4 - 8T^3 + 3T^2 + 3*T + 1
$79$	\( T^{6} \) T^6
$83$	\( T^{6} + 3 T^{4} + \cdots + 1 \) T^6 + 3T^4 - 2T^3 + 9T^2 - 3T + 1
$89$	\( T^{6} - T^{3} + 1 \) T^6 - T^3 + 1
$97$	\( T^{6} - 3 T^{5} + \cdots + 1 \) T^6 - 3T^5 + 6T^4 - 8T^3 + 3T^2 + 3*T + 1
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