LMFDB - Newform orbit 460.1.n.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,1,Mod(39,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 8]))

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

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

chi := DirichletCharacter("460.39");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	460.n (of order $22$, degree $10$, 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:	$0.229569905811$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{11}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{11} - \cdots)$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$\zeta_{22}^{10}$

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} $

39.1

0.654861	+	0.755750i
0.654861	−	0.755750i
−0.415415	+	0.909632i
0.959493	−	0.281733i
−0.841254	−	0.540641i
0.959493	+	0.281733i
−0.415415	−	0.909632i
0.142315	−	0.989821i
0.142315	+	0.989821i
−0.841254	+	0.540641i

−0.654861

0.755750i

−1.10181

0.708089i

−0.142315

−

0.989821i

0.415415

0.909632i

0.186393

−

1.29639i

1.84125

−

0.540641i

0.841254

0.540641i

0.297176

−

0.650724i

−0.959493

−

0.281733i

59.1

−0.654861

−

0.755750i

−1.10181

−

0.708089i

−0.142315

0.989821i

0.415415

−

0.909632i

0.186393

1.29639i

1.84125

0.540641i

0.841254

−

0.540641i

0.297176

0.650724i

−0.959493

0.281733i

119.1

0.415415

0.909632i

−0.797176

0.234072i

−0.654861

0.755750i

0.841254

0.540641i

−0.544078

−

0.627899i

0.0405070

0.281733i

−0.959493

−

0.281733i

−0.260554

0.167448i

−0.142315

0.989821i

179.1

−0.959493

−

0.281733i

1.25667

−

1.45027i

0.841254

0.540641i

−0.142315

0.989821i

−1.61435

1.03748i

0.345139

0.755750i

−0.654861

−

0.755750i

−0.381761

−

2.65520i

0.415415

−

0.909632i

219.1

0.841254

−

0.540641i

−0.239446

1.66538i

0.415415

−

0.909632i

−0.959493

0.281733i

0.698939

1.53046i

0.857685

0.989821i

−0.142315

−

0.989821i

−1.75667

−

0.515804i

−0.654861

0.755750i

239.1

−0.959493

0.281733i

1.25667

1.45027i

0.841254

−

0.540641i

−0.142315

−

0.989821i

−1.61435

−

1.03748i

0.345139

−

0.755750i

−0.654861

0.755750i

−0.381761

2.65520i

0.415415

0.909632i

259.1

0.415415

−

0.909632i

−0.797176

−

0.234072i

−0.654861

−

0.755750i

0.841254

−

0.540641i

−0.544078

0.627899i

0.0405070

−

0.281733i

−0.959493

0.281733i

−0.260554

−

0.167448i

−0.142315

−

0.989821i

279.1

−0.142315

−

0.989821i

−0.118239

0.258908i

−0.959493

0.281733i

−0.654861

0.755750i

0.273100

0.0801894i

1.41542

−

0.909632i

0.415415

0.909632i

0.601808

0.694523i

0.841254

0.540641i

399.1

−0.142315

0.989821i

−0.118239

−

0.258908i

−0.959493

−

0.281733i

−0.654861

−

0.755750i

0.273100

−

0.0801894i

1.41542

0.909632i

0.415415

−

0.909632i

0.601808

−

0.694523i

0.841254

−

0.540641i

439.1

0.841254

0.540641i

−0.239446

−

1.66538i

0.415415

0.909632i

−0.959493

−

0.281733i

0.698939

−

1.53046i

0.857685

−

0.989821i

−0.142315

0.989821i

−1.75667

0.515804i

−0.654861

−

0.755750i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
20.d	odd	2	1	CM by $\Q(\sqrt{-5}) $
23.c	even	11	1	inner
460.n	odd	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	460.1.n.a	✓	10
4.b	odd	2	1		460.1.n.b	yes	10
5.b	even	2	1		460.1.n.b	yes	10
5.c	odd	4	2		2300.1.bf.a		20
20.d	odd	2	1	CM	460.1.n.a	✓	10
20.e	even	4	2		2300.1.bf.a		20
23.c	even	11	1	inner	460.1.n.a	✓	10
92.g	odd	22	1		460.1.n.b	yes	10
115.j	even	22	1		460.1.n.b	yes	10
115.k	odd	44	2		2300.1.bf.a		20
460.n	odd	22	1	inner	460.1.n.a	✓	10
460.w	even	44	2		2300.1.bf.a		20

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
460.1.n.a	✓	10	1.a	even	1	1	trivial
460.1.n.a	✓	10	20.d	odd	2	1	CM
460.1.n.a	✓	10	23.c	even	11	1	inner
460.1.n.a	✓	10	460.n	odd	22	1	inner
460.1.n.b	yes	10	4.b	odd	2	1
460.1.n.b	yes	10	5.b	even	2	1
460.1.n.b	yes	10	92.g	odd	22	1
460.1.n.b	yes	10	115.j	even	22	1
2300.1.bf.a		20	5.c	odd	4	2
2300.1.bf.a		20	20.e	even	4	2
2300.1.bf.a		20	115.k	odd	44	2
2300.1.bf.a		20	460.w	even	44	2

This newform subspace can be constructed as the kernel of the linear operator $ T_{3}^{10} + 2T_{3}^{9} + 4T_{3}^{8} + 8T_{3}^{7} + 16T_{3}^{6} + 32T_{3}^{5} + 53T_{3}^{4} + 51T_{3}^{3} + 25T_{3}^{2} + 6T_{3} + 1 $ T3^10 + 2*T3^9 + 4*T3^8 + 8*T3^7 + 16*T3^6 + 32*T3^5 + 53*T3^4 + 51*T3^3 + 25*T3^2 + 6*T3 + 1 acting on $S_{1}^{\mathrm{new}}(460, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T^{10} + T^{9} + \cdots + 1 $ T^10 + T^9 + T^8 + T^7 + T^6 + T^5 + T^4 + T^3 + T^2 + T + 1
$3$	$ T^{10} + 2 T^{9} + \cdots + 1 $ T^10 + 2T^9 + 4T^8 + 8T^7 + 16T^6 + 32T^5 + 53T^4 + 51T^3 + 25T^2 + 6*T + 1
$5$	$ T^{10} + T^{9} + \cdots + 1 $ T^10 + T^9 + T^8 + T^7 + T^6 + T^5 + T^4 + T^3 + T^2 + T + 1
$7$	$ T^{10} - 9 T^{9} + \cdots + 1 $ T^10 - 9T^9 + 37T^8 - 91T^7 + 148T^6 - 166T^5 + 130T^4 - 70T^3 + 25T^2 - 5*T + 1
$11$	$ T^{10} $ T^10
$13$	$ T^{10} $ T^10
$17$	$ T^{10} $ T^10
$19$	$ T^{10} $ T^10
$23$	$ T^{10} + T^{9} + \cdots + 1 $ T^10 + T^9 + T^8 + T^7 + T^6 + T^5 + T^4 + T^3 + T^2 + T + 1
$29$	$ T^{10} + 2 T^{9} + \cdots + 1 $ T^10 + 2T^9 + 4T^8 - 3T^7 - 6T^6 - 12T^5 + 9T^4 + 7T^3 + 14T^2 + 6*T + 1
$31$	$ T^{10} $ T^10
$37$	$ T^{10} $ T^10
$41$	$ T^{10} + 2 T^{9} + \cdots + 1 $ T^10 + 2T^9 + 4T^8 - 3T^7 - 6T^6 - 12T^5 + 9T^4 + 7T^3 + 14T^2 + 6*T + 1
$43$	$ T^{10} + 2 T^{9} + \cdots + 1 $ T^10 + 2T^9 + 4T^8 - 3T^7 - 6T^6 - 12T^5 + 9T^4 + 7T^3 + 14T^2 + 6*T + 1
$47$	$ (T^{5} + T^{4} - 4 T^{3} + \cdots + 1)^{2} $ (T^5 + T^4 - 4T^3 - 3T^2 + 3*T + 1)^2
$53$	$ T^{10} $ T^10
$59$	$ T^{10} $ T^10
$61$	$ T^{10} + 2 T^{9} + \cdots + 1 $ T^10 + 2T^9 + 4T^8 - 3T^7 - 6T^6 - 12T^5 + 9T^4 + 7T^3 + 14T^2 + 6*T + 1
$67$	$ T^{10} + 2 T^{9} + \cdots + 1 $ T^10 + 2T^9 + 4T^8 - 3T^7 - 6T^6 - 12T^5 + 9T^4 + 7T^3 + 14T^2 + 6*T + 1
$71$	$ T^{10} $ T^10
$73$	$ T^{10} $ T^10
$79$	$ T^{10} $ T^10
$83$	$ T^{10} + 2 T^{9} + \cdots + 1 $ T^10 + 2T^9 + 4T^8 + 8T^7 + 16T^6 + 10T^5 + 20T^4 + 7T^3 + 3T^2 - 5*T + 1
$89$	$ T^{10} + 2 T^{9} + \cdots + 1 $ T^10 + 2T^9 + 4T^8 + 8T^7 + 16T^6 + 32T^5 + 53T^4 + 51T^3 + 25T^2 + 6*T + 1
$97$	$ T^{10} $ T^10
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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	460.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\( q + \zeta_{22}^{10} q^{2} + (\zeta_{22}^{4} + \zeta_{22}^{2}) q^{3} - \zeta_{22}^{9} q^{4} - \zeta_{22}^{5} q^{5} + ( - \zeta_{22}^{3} - \zeta_{22}) q^{6} + ( - \zeta_{22}^{3} + 1) q^{7} + \zeta_{22}^{8} q^{8} + (\zeta_{22}^{8} + \cdots + \zeta_{22}^{4}) q^{9} +O(q^{10}) \) q + z^10 * q^2 + (z^4 + z^2) * q^3 - z^9 * q^4 - z^5 * q^5 + (-z^3 - z) * q^6 + (-z^3 + 1) * q^7 + z^8 * q^8 + (z^8 + z^6 + z^4) * q^9	\( q + \zeta_{22}^{10} q^{2} + (\zeta_{22}^{4} + \zeta_{22}^{2}) q^{3} - \zeta_{22}^{9} q^{4} - \zeta_{22}^{5} q^{5} + ( - \zeta_{22}^{3} - \zeta_{22}) q^{6} + ( - \zeta_{22}^{3} + 1) q^{7} + \zeta_{22}^{8} q^{8} + (\zeta_{22}^{8} + \cdots + \zeta_{22}^{4}) q^{9} + \cdots + (\zeta_{22}^{10} + \cdots + \zeta_{22}^{2}) q^{98} +O(q^{100}) \) q + z^10 * q^2 + (z^4 + z^2) * q^3 - z^9 * q^4 - z^5 * q^5 + (-z^3 - z) * q^6 + (-z^3 + 1) * q^7 + z^8 * q^8 + (z^8 + z^6 + z^4) * q^9 + z^4 * q^10 + (z^2 + 1) * q^12 + (z^10 + z^2) * q^14 + (-z^9 - z^7) * q^15 - z^7 * q^16 + (-z^7 - z^5 - z^3) * q^18 - z^3 * q^20 + (-z^7 - z^5 + z^4 + z^2) * q^21 + z^10 * q^23 + (z^10 - z) * q^24 + z^10 * q^25 + (z^10 + z^8 + z^6 - z) * q^27 + (-z^9 - z) * q^28 + (z^8 - z^7) * q^29 + (z^8 + z^6) * q^30 + z^6 * q^32 + (z^8 - z^5) * q^35 + (z^6 + z^4 + z^2) * q^36 + z^2 * q^40 + (-z^9 - z) * q^41 + (z^6 + z^4 - z^3 - z) * q^42 + (-z^5 - z) * q^43 + (-z^9 + z^2 + 1) * q^45 - z^9 * q^46 + (z^6 - z^5) * q^47 + (-z^9 + 1) * q^48 + (z^6 - z^3 + 1) * q^49 - z^9 * q^50 + (-z^9 - z^7 - z^5 + 1) * q^54 + (z^8 + 1) * q^56 + (-z^7 + z^6) * q^58 + (-z^7 - z^5) * q^60 + (z^10 + z^6) * q^61 + (-z^9 + z^8 - z^7 + z^6 + z^4 + 1) * q^63 - z^5 * q^64 + (-z^7 + z^2) * q^67 + (-z^3 - z) * q^69 + (-z^7 + z^4) * q^70 + (-z^5 - z^3 - z) * q^72 + (-z^3 - z) * q^75 - z * q^80 + (z^10 + z^8 - z^5 + z^3 + z) * q^81 + (z^8 + 1) * q^82 + (-z^9 - z^3) * q^83 + (-z^5 - z^3 + z^2 + 1) * q^84 + (z^4 + 1) * q^86 + (z^10 - z^9 - z + 1) * q^87 + (z^4 + z^2) * q^89 + (z^10 + z^8 - z) * q^90 + z^8 * q^92 + (-z^5 + z^4) * q^94 + (z^10 + z^8) * q^96 + (z^10 - z^5 + z^2) * q^98
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} + 9 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q - q^2 - 2 * q^3 - q^4 - q^5 - 2 * q^6 + 9 * q^7 - q^8 - 3 * q^9	\( 10 q - q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} + 9 q^{7} - q^{8} - 3 q^{9} - q^{10} + 9 q^{12} - 2 q^{14} - 2 q^{15} - q^{16} - 3 q^{18} - q^{20} - 4 q^{21} - q^{23} - 2 q^{24} - q^{25} - 4 q^{27} - 2 q^{28} - 2 q^{29} - 2 q^{30} - q^{32} - 2 q^{35} - 3 q^{36} - q^{40} - 2 q^{41} - 4 q^{42} - 2 q^{43} + 8 q^{45} - q^{46} - 2 q^{47} + 9 q^{48} + 8 q^{49} - q^{50} + 7 q^{54} + 9 q^{56} - 2 q^{58} - 2 q^{60} - 2 q^{61} + 5 q^{63} - q^{64} - 2 q^{67} - 2 q^{69} - 2 q^{70} - 3 q^{72} - 2 q^{75} - q^{80} - 5 q^{81} + 9 q^{82} - 2 q^{83} + 7 q^{84} + 9 q^{86} + 7 q^{87} - 2 q^{89} - 3 q^{90} - q^{92} - 2 q^{94} - 2 q^{96} - 3 q^{98}+O(q^{100}) \) 10 * q - q^2 - 2 * q^3 - q^4 - q^5 - 2 * q^6 + 9 * q^7 - q^8 - 3 * q^9 - q^10 + 9 * q^12 - 2 * q^14 - 2 * q^15 - q^16 - 3 * q^18 - q^20 - 4 * q^21 - q^23 - 2 * q^24 - q^25 - 4 * q^27 - 2 * q^28 - 2 * q^29 - 2 * q^30 - q^32 - 2 * q^35 - 3 * q^36 - q^40 - 2 * q^41 - 4 * q^42 - 2 * q^43 + 8 * q^45 - q^46 - 2 * q^47 + 9 * q^48 + 8 * q^49 - q^50 + 7 * q^54 + 9 * q^56 - 2 * q^58 - 2 * q^60 - 2 * q^61 + 5 * q^63 - q^64 - 2 * q^67 - 2 * q^69 - 2 * q^70 - 3 * q^72 - 2 * q^75 - q^80 - 5 * q^81 + 9 * q^82 - 2 * q^83 + 7 * q^84 + 9 * q^86 + 7 * q^87 - 2 * q^89 - 3 * q^90 - q^92 - 2 * q^94 - 2 * q^96 - 3 * q^98

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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	460.1.n.a

Level	$460$
Weight	$1$
Character orbit	460.n
Analytic conductor	$0.230$
Analytic rank	$0$
Dimension	$10$
Projective image	$D_{11}$
CM discriminant	-20
Inner twists	$4$

Self dual:	no
Analytic conductor:	\(0.229569905811\)
Analytic rank:	\(0\)
Dimension:	\(10\)
Coefficient field:	\(\Q(\zeta_{22})\)
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	\( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Projective image:	\(D_{11}\)
Projective field:	Galois closure of \(\mathbb{Q}[x]/(x^{11} - \cdots)\)

\(n\)	\(231\)	\(277\)	\(281\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(\zeta_{22}^{10}\)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 39.1
Significant digits:
Format:

$p$	$F_p(T)$
$2$	\( T^{10} + T^{9} + \cdots + 1 \) T^10 + T^9 + T^8 + T^7 + T^6 + T^5 + T^4 + T^3 + T^2 + T + 1
$3$	\( T^{10} + 2 T^{9} + \cdots + 1 \) T^10 + 2T^9 + 4T^8 + 8T^7 + 16T^6 + 32T^5 + 53T^4 + 51T^3 + 25T^2 + 6*T + 1
$5$	\( T^{10} + T^{9} + \cdots + 1 \) T^10 + T^9 + T^8 + T^7 + T^6 + T^5 + T^4 + T^3 + T^2 + T + 1
$7$	\( T^{10} - 9 T^{9} + \cdots + 1 \) T^10 - 9T^9 + 37T^8 - 91T^7 + 148T^6 - 166T^5 + 130T^4 - 70T^3 + 25T^2 - 5*T + 1
$11$	\( T^{10} \) T^10
$13$	\( T^{10} \) T^10
$17$	\( T^{10} \) T^10
$19$	\( T^{10} \) T^10
$23$	\( T^{10} + T^{9} + \cdots + 1 \) T^10 + T^9 + T^8 + T^7 + T^6 + T^5 + T^4 + T^3 + T^2 + T + 1
$29$	\( T^{10} + 2 T^{9} + \cdots + 1 \) T^10 + 2T^9 + 4T^8 - 3T^7 - 6T^6 - 12T^5 + 9T^4 + 7T^3 + 14T^2 + 6*T + 1
$31$	\( T^{10} \) T^10
$37$	\( T^{10} \) T^10
$41$	\( T^{10} + 2 T^{9} + \cdots + 1 \) T^10 + 2T^9 + 4T^8 - 3T^7 - 6T^6 - 12T^5 + 9T^4 + 7T^3 + 14T^2 + 6*T + 1
$43$	\( T^{10} + 2 T^{9} + \cdots + 1 \) T^10 + 2T^9 + 4T^8 - 3T^7 - 6T^6 - 12T^5 + 9T^4 + 7T^3 + 14T^2 + 6*T + 1
$47$	\( (T^{5} + T^{4} - 4 T^{3} + \cdots + 1)^{2} \) (T^5 + T^4 - 4T^3 - 3T^2 + 3*T + 1)^2
$53$	\( T^{10} \) T^10
$59$	\( T^{10} \) T^10
$61$	\( T^{10} + 2 T^{9} + \cdots + 1 \) T^10 + 2T^9 + 4T^8 - 3T^7 - 6T^6 - 12T^5 + 9T^4 + 7T^3 + 14T^2 + 6*T + 1
$67$	\( T^{10} + 2 T^{9} + \cdots + 1 \) T^10 + 2T^9 + 4T^8 - 3T^7 - 6T^6 - 12T^5 + 9T^4 + 7T^3 + 14T^2 + 6*T + 1
$71$	\( T^{10} \) T^10
$73$	\( T^{10} \) T^10
$79$	\( T^{10} \) T^10
$83$	\( T^{10} + 2 T^{9} + \cdots + 1 \) T^10 + 2T^9 + 4T^8 + 8T^7 + 16T^6 + 10T^5 + 20T^4 + 7T^3 + 3T^2 - 5*T + 1
$89$	\( T^{10} + 2 T^{9} + \cdots + 1 \) T^10 + 2T^9 + 4T^8 + 8T^7 + 16T^6 + 32T^5 + 53T^4 + 51T^3 + 25T^2 + 6*T + 1
$97$	\( T^{10} \) T^10
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