LMFDB - Newform orbit 435.3.b.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,3,Mod(434,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("435.434");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	435.b (of order $2$, degree $1$, 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:	yes
Analytic conductor:	$11.8528914997$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$ q - 3 q^{3} + 4 q^{4} + 5 q^{5} + 9 q^{9}+O(q^{10}) $

$ q - 3 q^{3} + 4 q^{4} + 5 q^{5} + 9 q^{9} + 7 q^{11} - 12 q^{12} - 15 q^{15} + 16 q^{16} + 20 q^{20} - 41 q^{23} + 25 q^{25} - 27 q^{27} + 29 q^{29} - 21 q^{33} + 36 q^{36} + 71 q^{37} - 53 q^{41} + 59 q^{43} + 28 q^{44} + 45 q^{45} - 48 q^{48} + 49 q^{49} + 19 q^{53} + 35 q^{55} - 60 q^{60} + 64 q^{64} + 123 q^{69} - q^{73} - 75 q^{75} + 80 q^{80} + 81 q^{81} + 79 q^{83} - 87 q^{87} - 62 q^{89} - 164 q^{92} - 49 q^{97} + 63 q^{99}+O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$1$	$1$	$1$

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} $

434.1

−3.00000

4.00000

5.00000

9.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
435.b	odd	2	1	CM by $\Q(\sqrt{-435}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	435.3.b.b	yes	1
3.b	odd	2	1		435.3.b.a	✓	1
5.b	even	2	1		435.3.b.c	yes	1
15.d	odd	2	1		435.3.b.d	yes	1
29.b	even	2	1		435.3.b.d	yes	1
87.d	odd	2	1		435.3.b.c	yes	1
145.d	even	2	1		435.3.b.a	✓	1
435.b	odd	2	1	CM	435.3.b.b	yes	1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
435.3.b.a	✓	1	3.b	odd	2	1
435.3.b.a	✓	1	145.d	even	2	1
435.3.b.b	yes	1	1.a	even	1	1	trivial
435.3.b.b	yes	1	435.b	odd	2	1	CM
435.3.b.c	yes	1	5.b	even	2	1
435.3.b.c	yes	1	87.d	odd	2	1
435.3.b.d	yes	1	15.d	odd	2	1
435.3.b.d	yes	1	29.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{3}^{\mathrm{new}}(435, [\chi])$:

$ T_{2} $

$ T_{11} - 7 $

$ T_{23} + 41 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T + 3 $ T + 3
$5$	$ T - 5 $ T - 5
$7$	$ T $ T
$11$	$ T - 7 $ T - 7
$13$	$ T $ T
$17$	$ T $ T
$19$	$ T $ T
$23$	$ T + 41 $ T + 41
$29$	$ T - 29 $ T - 29
$31$	$ T $ T
$37$	$ T - 71 $ T - 71
$41$	$ T + 53 $ T + 53
$43$	$ T - 59 $ T - 59
$47$	$ T $ T
$53$	$ T - 19 $ T - 19
$59$	$ T $ T
$61$	$ T $ T
$67$	$ T $ T
$71$	$ T $ T
$73$	$ T + 1 $ T + 1
$79$	$ T $ T
$83$	$ T - 79 $ T - 79
$89$	$ T + 62 $ T + 62
$97$	$ T + 49 $ T + 49
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Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	435.b (of order \(2\), degree \(1\), minimal)

\(n\)	\(31\)	\(146\)	\(262\)
\(\chi(n)\)	\(1\)	\(1\)	\(1\)

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