LMFDB - Newform orbit 275.2.a.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(1,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, 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("275.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$275 = 5^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	275.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:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 11)
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 + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} - 2 q^{9} + q^{11} + 2 q^{12} - 4 q^{13} + 4 q^{14} - 4 q^{16} + 2 q^{17} - 4 q^{18} + 2 q^{21} + 2 q^{22} + q^{23} - 8 q^{26} - 5 q^{27} + 4 q^{28}+ \cdots - 2 q^{99}+O(q^{100})

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

2.00000

1.00000

2.00000

−2.00000

Atkin-Lehner signs

$p$	Sign
$5$	$+1$
$11$	$-1$

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	275.2.a.b		1
3.b	odd	2	1		2475.2.a.a		1
4.b	odd	2	1		4400.2.a.i		1
5.b	even	2	1		11.2.a.a	✓	1
5.c	odd	4	2		275.2.b.a		2
11.b	odd	2	1		3025.2.a.a		1
15.d	odd	2	1		99.2.a.d		1
15.e	even	4	2		2475.2.c.a		2
20.d	odd	2	1		176.2.a.b		1
20.e	even	4	2		4400.2.b.h		2
35.c	odd	2	1		539.2.a.a		1
35.i	odd	6	2		539.2.e.g		2
35.j	even	6	2		539.2.e.h		2
40.e	odd	2	1		704.2.a.c		1
40.f	even	2	1		704.2.a.h		1
45.h	odd	6	2		891.2.e.b		2
45.j	even	6	2		891.2.e.k		2
55.d	odd	2	1		121.2.a.d		1
55.h	odd	10	4		121.2.c.a		4
55.j	even	10	4		121.2.c.e		4
60.h	even	2	1		1584.2.a.g		1
65.d	even	2	1		1859.2.a.b		1
80.k	odd	4	2		2816.2.c.f		2
80.q	even	4	2		2816.2.c.j		2
85.c	even	2	1		3179.2.a.a		1
95.d	odd	2	1		3971.2.a.b		1
105.g	even	2	1		4851.2.a.t		1
115.c	odd	2	1		5819.2.a.a		1
120.i	odd	2	1		6336.2.a.br		1
120.m	even	2	1		6336.2.a.bu		1
140.c	even	2	1		8624.2.a.j		1
145.d	even	2	1		9251.2.a.d		1
165.d	even	2	1		1089.2.a.b		1
220.g	even	2	1		1936.2.a.i		1
385.h	even	2	1		5929.2.a.h		1
440.c	even	2	1		7744.2.a.k		1
440.o	odd	2	1		7744.2.a.x		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
11.2.a.a	✓	1	5.b	even	2	1
99.2.a.d		1	15.d	odd	2	1
121.2.a.d		1	55.d	odd	2	1
121.2.c.a		4	55.h	odd	10	4
121.2.c.e		4	55.j	even	10	4
176.2.a.b		1	20.d	odd	2	1
275.2.a.b		1	1.a	even	1	1	trivial
275.2.b.a		2	5.c	odd	4	2
539.2.a.a		1	35.c	odd	2	1
539.2.e.g		2	35.i	odd	6	2
539.2.e.h		2	35.j	even	6	2
704.2.a.c		1	40.e	odd	2	1
704.2.a.h		1	40.f	even	2	1
891.2.e.b		2	45.h	odd	6	2
891.2.e.k		2	45.j	even	6	2
1089.2.a.b		1	165.d	even	2	1
1584.2.a.g		1	60.h	even	2	1
1859.2.a.b		1	65.d	even	2	1
1936.2.a.i		1	220.g	even	2	1
2475.2.a.a		1	3.b	odd	2	1
2475.2.c.a		2	15.e	even	4	2
2816.2.c.f		2	80.k	odd	4	2
2816.2.c.j		2	80.q	even	4	2
3025.2.a.a		1	11.b	odd	2	1
3179.2.a.a		1	85.c	even	2	1
3971.2.a.b		1	95.d	odd	2	1
4400.2.a.i		1	4.b	odd	2	1
4400.2.b.h		2	20.e	even	4	2
4851.2.a.t		1	105.g	even	2	1
5819.2.a.a		1	115.c	odd	2	1
5929.2.a.h		1	385.h	even	2	1
6336.2.a.br		1	120.i	odd	2	1
6336.2.a.bu		1	120.m	even	2	1
7744.2.a.k		1	440.c	even	2	1
7744.2.a.x		1	440.o	odd	2	1
8624.2.a.j		1	140.c	even	2	1
9251.2.a.d		1	145.d	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2} - 2$ T2 - 2 acting on $S_{2}^{\mathrm{new}}(\Gamma_0(275))$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 2$ T - 2
$3$	$T - 1$ T - 1
$5$	$T$ T
$7$	$T - 2$ T - 2
$11$	$T - 1$ T - 1
$13$	$T + 4$ T + 4
$17$	$T - 2$ T - 2
$19$	$T$ T
$23$	$T - 1$ T - 1
$29$	$T$ T
$31$	$T - 7$ T - 7
$37$	$T + 3$ T + 3
$41$	$T + 8$ T + 8
$43$	$T - 6$ T - 6
$47$	$T + 8$ T + 8
$53$	$T - 6$ T - 6
$59$	$T - 5$ T - 5
$61$	$T - 12$ T - 12
$67$	$T - 7$ T - 7
$71$	$T + 3$ T + 3
$73$	$T + 4$ T + 4
$79$	$T + 10$ T + 10
$83$	$T - 6$ T - 6
$89$	$T - 15$ T - 15
$97$	$T - 7$ T - 7
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