LMFDB - Newform orbit 234.2.a.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(1,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("234.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.a (trivial)

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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
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 - q^{2} + q^{4} + q^{5} + q^{7} - q^{8}+O(q^{10}) $

$ q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + 2 q^{11} - q^{13} - q^{14} + q^{16} + 3 q^{17} + 6 q^{19} + q^{20} - 2 q^{22} + 4 q^{23} - 4 q^{25} + q^{26} + q^{28} - 2 q^{29} + 4 q^{31} - q^{32} - 3 q^{34} + q^{35} + 3 q^{37} - 6 q^{38} - q^{40} - 5 q^{43} + 2 q^{44} - 4 q^{46} - 13 q^{47} - 6 q^{49} + 4 q^{50} - q^{52} - 12 q^{53} + 2 q^{55} - q^{56} + 2 q^{58} + 10 q^{59} - 8 q^{61} - 4 q^{62} + q^{64} - q^{65} - 2 q^{67} + 3 q^{68} - q^{70} + 5 q^{71} - 10 q^{73} - 3 q^{74} + 6 q^{76} + 2 q^{77} - 4 q^{79} + q^{80} + 3 q^{85} + 5 q^{86} - 2 q^{88} - 6 q^{89} - q^{91} + 4 q^{92} + 13 q^{94} + 6 q^{95} + 14 q^{97} + 6 q^{98}+O(q^{100}) $

Display 100 coefficients 10 coefficients

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

−1.00000

1.00000

−1.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$1$
$3$	$-1$
$13$	$1$

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	234.2.a.b		1
3.b	odd	2	1		26.2.a.b	✓	1
4.b	odd	2	1		1872.2.a.m		1
5.b	even	2	1		5850.2.a.bn		1
5.c	odd	4	2		5850.2.e.v		2
8.b	even	2	1		7488.2.a.w		1
8.d	odd	2	1		7488.2.a.v		1
9.c	even	3	2		2106.2.e.t		2
9.d	odd	6	2		2106.2.e.h		2
12.b	even	2	1		208.2.a.d		1
13.b	even	2	1		3042.2.a.l		1
13.d	odd	4	2		3042.2.b.f		2
15.d	odd	2	1		650.2.a.g		1
15.e	even	4	2		650.2.b.a		2
21.c	even	2	1		1274.2.a.o		1
21.g	even	6	2		1274.2.f.a		2
21.h	odd	6	2		1274.2.f.l		2
24.f	even	2	1		832.2.a.a		1
24.h	odd	2	1		832.2.a.j		1
33.d	even	2	1		3146.2.a.a		1
39.d	odd	2	1		338.2.a.a		1
39.f	even	4	2		338.2.b.a		2
39.h	odd	6	2		338.2.c.g		2
39.i	odd	6	2		338.2.c.c		2
39.k	even	12	4		338.2.e.d		4
48.i	odd	4	2		3328.2.b.g		2
48.k	even	4	2		3328.2.b.k		2
51.c	odd	2	1		7514.2.a.i		1
57.d	even	2	1		9386.2.a.f		1
60.h	even	2	1		5200.2.a.c		1
156.h	even	2	1		2704.2.a.n		1
156.l	odd	4	2		2704.2.f.j		2
195.e	odd	2	1		8450.2.a.y		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
26.2.a.b	✓	1	3.b	odd	2	1
208.2.a.d		1	12.b	even	2	1
234.2.a.b		1	1.a	even	1	1	trivial
338.2.a.a		1	39.d	odd	2	1
338.2.b.a		2	39.f	even	4	2
338.2.c.c		2	39.i	odd	6	2
338.2.c.g		2	39.h	odd	6	2
338.2.e.d		4	39.k	even	12	4
650.2.a.g		1	15.d	odd	2	1
650.2.b.a		2	15.e	even	4	2
832.2.a.a		1	24.f	even	2	1
832.2.a.j		1	24.h	odd	2	1
1274.2.a.o		1	21.c	even	2	1
1274.2.f.a		2	21.g	even	6	2
1274.2.f.l		2	21.h	odd	6	2
1872.2.a.m		1	4.b	odd	2	1
2106.2.e.h		2	9.d	odd	6	2
2106.2.e.t		2	9.c	even	3	2
2704.2.a.n		1	156.h	even	2	1
2704.2.f.j		2	156.l	odd	4	2
3042.2.a.l		1	13.b	even	2	1
3042.2.b.f		2	13.d	odd	4	2
3146.2.a.a		1	33.d	even	2	1
3328.2.b.g		2	48.i	odd	4	2
3328.2.b.k		2	48.k	even	4	2
5200.2.a.c		1	60.h	even	2	1
5850.2.a.bn		1	5.b	even	2	1
5850.2.e.v		2	5.c	odd	4	2
7488.2.a.v		1	8.d	odd	2	1
7488.2.a.w		1	8.b	even	2	1
7514.2.a.i		1	51.c	odd	2	1
8450.2.a.y		1	195.e	odd	2	1
9386.2.a.f		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 $S_{2}^{\mathrm{new}}(\Gamma_0(234))$:

$ T_{5} - 1 $

$ T_{7} - 1 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 1 $ T + 1
$3$	$ T $ T
$5$	$ T - 1 $ T - 1
$7$	$ T - 1 $ T - 1
$11$	$ T - 2 $ T - 2
$13$	$ T + 1 $ T + 1
$17$	$ T - 3 $ T - 3
$19$	$ T - 6 $ T - 6
$23$	$ T - 4 $ T - 4
$29$	$ T + 2 $ T + 2
$31$	$ T - 4 $ T - 4
$37$	$ T - 3 $ T - 3
$41$	$ T $ T
$43$	$ T + 5 $ T + 5
$47$	$ T + 13 $ T + 13
$53$	$ T + 12 $ T + 12
$59$	$ T - 10 $ T - 10
$61$	$ T + 8 $ T + 8
$67$	$ T + 2 $ T + 2
$71$	$ T - 5 $ T - 5
$73$	$ T + 10 $ T + 10
$79$	$ T + 4 $ T + 4
$83$	$ T $ T
$89$	$ T + 6 $ T + 6
$97$	$ T - 14 $ T - 14
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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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
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