LMFDB - Newform orbit 175.9.d.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,9,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, 9, names="a")

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

chi := DirichletCharacter("175.76");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
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:	$71.2912567607$
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 + 31 q^{2} + 705 q^{4} - 2401 q^{7} + 13919 q^{8} + 6561 q^{9}+O(q^{10}) $

$ q + 31 q^{2} + 705 q^{4} - 2401 q^{7} + 13919 q^{8} + 6561 q^{9} + 13154 q^{11} - 74431 q^{14} + 251009 q^{16} + 203391 q^{18} + 407774 q^{22} + 20926 q^{23} - 1692705 q^{28} + 108194 q^{29} + 4218015 q^{32} + 4625505 q^{36} + 2073886 q^{37} + 6726046 q^{43} + 9273570 q^{44} + 648706 q^{46} + 5764801 q^{49} - 15377762 q^{53} - 33419519 q^{56} + 3354014 q^{58} - 15752961 q^{63} + 66500161 q^{64} + 15839326 q^{67} - 42331966 q^{71} + 91322559 q^{72} + 64290466 q^{74} - 31582754 q^{77} - 64606846 q^{79} + 43046721 q^{81} + 208507426 q^{86} + 183090526 q^{88} + 14752830 q^{92} + 178708831 q^{98} + 86303394 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

31.0000

705.000

−2401.00

13919.0

6561.00

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	175.9.d.a		1
5.b	even	2	1		7.9.b.a	✓	1
5.c	odd	4	2		175.9.c.a		2
7.b	odd	2	1	CM	175.9.d.a		1
15.d	odd	2	1		63.9.d.a		1
20.d	odd	2	1		112.9.c.a		1
35.c	odd	2	1		7.9.b.a	✓	1
35.f	even	4	2		175.9.c.a		2
35.i	odd	6	2		49.9.d.a		2
35.j	even	6	2		49.9.d.a		2
105.g	even	2	1		63.9.d.a		1
140.c	even	2	1		112.9.c.a		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7.9.b.a	✓	1	5.b	even	2	1
7.9.b.a	✓	1	35.c	odd	2	1
49.9.d.a		2	35.i	odd	6	2
49.9.d.a		2	35.j	even	6	2
63.9.d.a		1	15.d	odd	2	1
63.9.d.a		1	105.g	even	2	1
112.9.c.a		1	20.d	odd	2	1
112.9.c.a		1	140.c	even	2	1
175.9.c.a		2	5.c	odd	4	2
175.9.c.a		2	35.f	even	4	2
175.9.d.a		1	1.a	even	1	1	trivial
175.9.d.a		1	7.b	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{2} - 31 $ T2 - 31 acting on $S_{9}^{\mathrm{new}}(175, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 31 $ T - 31
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T + 2401 $ T + 2401
$11$	$ T - 13154 $ T - 13154
$13$	$ T $ T
$17$	$ T $ T
$19$	$ T $ T
$23$	$ T - 20926 $ T - 20926
$29$	$ T - 108194 $ T - 108194
$31$	$ T $ T
$37$	$ T - 2073886 $ T - 2073886
$41$	$ T $ T
$43$	$ T - 6726046 $ T - 6726046
$47$	$ T $ T
$53$	$ T + 15377762 $ T + 15377762
$59$	$ T $ T
$61$	$ T $ T
$67$	$ T - 15839326 $ T - 15839326
$71$	$ T + 42331966 $ T + 42331966
$73$	$ T $ T
$79$	$ T + 64606846 $ T + 64606846
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T $ T
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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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	175.d (of order \(2\), degree \(1\), minimal)

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

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