LMFDB - Newform orbit 275.4.a.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,4,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, 4, names="a")

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

chi := DirichletCharacter("275.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$275 = 5^{2} \cdot 11$
Weight:	$k$	$=$	$4$
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:	$16.2255252516$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 55)
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} + 3 q^{3} - 7 q^{4} - 3 q^{6} + 9 q^{7} + 15 q^{8} - 18 q^{9} + 11 q^{11} - 21 q^{12} - 2 q^{13} - 9 q^{14} + 41 q^{16} - 21 q^{17} + 18 q^{18} - 85 q^{19} + 27 q^{21} - 11 q^{22} - 22 q^{23}+ \cdots - 198 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

−1.00000

3.00000

−7.00000

−3.00000

9.00000

15.0000

−18.0000

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	275.4.a.a		1
3.b	odd	2	1		2475.4.a.h		1
5.b	even	2	1		55.4.a.a	✓	1
5.c	odd	4	2		275.4.b.a		2
15.d	odd	2	1		495.4.a.a		1
20.d	odd	2	1		880.4.a.j		1
55.d	odd	2	1		605.4.a.b		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
55.4.a.a	✓	1	5.b	even	2	1
275.4.a.a		1	1.a	even	1	1	trivial
275.4.b.a		2	5.c	odd	4	2
495.4.a.a		1	15.d	odd	2	1
605.4.a.b		1	55.d	odd	2	1
880.4.a.j		1	20.d	odd	2	1
2475.4.a.h		1	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2} + 1$ T2 + 1 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(275))$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 1$ T + 1
$3$	$T - 3$ T - 3
$5$	$T$ T
$7$	$T - 9$ T - 9
$11$	$T - 11$ T - 11
$13$	$T + 2$ T + 2
$17$	$T + 21$ T + 21
$19$	$T + 85$ T + 85
$23$	$T + 22$ T + 22
$29$	$T + 165$ T + 165
$31$	$T + 83$ T + 83
$37$	$T + 1$ T + 1
$41$	$T + 478$ T + 478
$43$	$T - 8$ T - 8
$47$	$T + 126$ T + 126
$53$	$T - 683$ T - 683
$59$	$T + 290$ T + 290
$61$	$T - 257$ T - 257
$67$	$T + 776$ T + 776
$71$	$T + 313$ T + 313
$73$	$T + 902$ T + 902
$79$	$T - 830$ T - 830
$83$	$T + 842$ T + 842
$89$	$T - 25$ T - 25
$97$	$T - 1784$ T - 1784
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