LMFDB - Newform orbit 175.5.d.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,5,Mod(76,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("175.76");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	175.d (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:	$18.0897435397$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
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 - q^{2} - 15 q^{4} - 49 q^{7} + 31 q^{8} + 81 q^{9}+O(q^{10}) $

$ q - q^{2} - 15 q^{4} - 49 q^{7} + 31 q^{8} + 81 q^{9} - 206 q^{11} + 49 q^{14} + 209 q^{16} - 81 q^{18} + 206 q^{22} + 734 q^{23} + 735 q^{28} + 1234 q^{29} - 705 q^{32} - 1215 q^{36} + 1294 q^{37} + 334 q^{43} + 3090 q^{44} - 734 q^{46} + 2401 q^{49} + 5582 q^{53} - 1519 q^{56} - 1234 q^{58} - 3969 q^{63} - 2639 q^{64} - 4946 q^{67} + 2914 q^{71} + 2511 q^{72} - 1294 q^{74} + 10094 q^{77} - 3646 q^{79} + 6561 q^{81} - 334 q^{86} - 6386 q^{88} - 11010 q^{92} - 2401 q^{98} - 16686 q^{99}+O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$1$

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} $

76.1

−1.00000

−15.0000

−49.0000

31.0000

81.0000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	CM by $\Q(\sqrt{-7}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	175.5.d.a		1
5.b	even	2	1		7.5.b.a	✓	1
5.c	odd	4	2		175.5.c.a		2
7.b	odd	2	1	CM	175.5.d.a		1
15.d	odd	2	1		63.5.d.a		1
20.d	odd	2	1		112.5.c.a		1
35.c	odd	2	1		7.5.b.a	✓	1
35.f	even	4	2		175.5.c.a		2
35.i	odd	6	2		49.5.d.a		2
35.j	even	6	2		49.5.d.a		2
40.e	odd	2	1		448.5.c.a		1
40.f	even	2	1		448.5.c.b		1
60.h	even	2	1		1008.5.f.a		1
105.g	even	2	1		63.5.d.a		1
140.c	even	2	1		112.5.c.a		1
280.c	odd	2	1		448.5.c.b		1
280.n	even	2	1		448.5.c.a		1
420.o	odd	2	1		1008.5.f.a		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7.5.b.a	✓	1	5.b	even	2	1
7.5.b.a	✓	1	35.c	odd	2	1
49.5.d.a		2	35.i	odd	6	2
49.5.d.a		2	35.j	even	6	2
63.5.d.a		1	15.d	odd	2	1
63.5.d.a		1	105.g	even	2	1
112.5.c.a		1	20.d	odd	2	1
112.5.c.a		1	140.c	even	2	1
175.5.c.a		2	5.c	odd	4	2
175.5.c.a		2	35.f	even	4	2
175.5.d.a		1	1.a	even	1	1	trivial
175.5.d.a		1	7.b	odd	2	1	CM
448.5.c.a		1	40.e	odd	2	1
448.5.c.a		1	280.n	even	2	1
448.5.c.b		1	40.f	even	2	1
448.5.c.b		1	280.c	odd	2	1
1008.5.f.a		1	60.h	even	2	1
1008.5.f.a		1	420.o	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 $S_{5}^{\mathrm{new}}(175, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 1 $ T + 1
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T + 49 $ T + 49
$11$	$ T + 206 $ T + 206
$13$	$ T $ T
$17$	$ T $ T
$19$	$ T $ T
$23$	$ T - 734 $ T - 734
$29$	$ T - 1234 $ T - 1234
$31$	$ T $ T
$37$	$ T - 1294 $ T - 1294
$41$	$ T $ T
$43$	$ T - 334 $ T - 334
$47$	$ T $ T
$53$	$ T - 5582 $ T - 5582
$59$	$ T $ T
$61$	$ T $ T
$67$	$ T + 4946 $ T + 4946
$71$	$ T - 2914 $ T - 2914
$73$	$ T $ T
$79$	$ T + 3646 $ T + 3646
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T $ T
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Overview	Random
Universe	Knowledge

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.d (of order \(2\), degree \(1\), minimal)

\(n\)	\(101\)	\(127\)
\(\chi(n)\)	\(-1\)	\(1\)

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