LMFDB - Newform orbit 2523.1.h.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2523,1,Mod(236,2523)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2523, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2523.236");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$2523 = 3 \cdot 29^{2}$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2523.h (of order $14$ , degree $6$ , not 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:	no
Analytic conductor:	$1.25914102687$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 87)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.87.1
Artin image:	$S_3\times C_{14}$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{42} - \cdots)$

$q$ -expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

The $q$ -expansion and trace form are shown below.

$f(q)$	$=$	$q + \zeta_{14}^{6} q^{2} - \zeta_{14}^{2} q^{3} + \zeta_{14} q^{6} - \zeta_{14}^{2} q^{7} - \zeta_{14}^{4} q^{8} + \zeta_{14}^{4} q^{9} - \zeta_{14}^{3} q^{11} + \zeta_{14}^{3} q^{13} + \zeta_{14} q^{14} + \cdots + q^{99} +O(q^{100})$ q + z^6 * q^2 - z^2 * q^3 + z * q^6 - z^2 * q^7 - z^4 * q^8 + z^4 * q^9 - z^3 * q^11 + z^3 * q^13 + z * q^14 + z^3 * q^16 + q^17 - z^3 * q^18 + z^4 * q^21 + z^2 * q^22 + z^6 * q^24 - z^5 * q^25 - z^2 * q^26 - z^6 * q^27 + z^5 * q^33 + z^6 * q^34 - z^5 * q^39 - 2 * q^41 - z^3 * q^42 - z^3 * q^47 - z^5 * q^48 + z^4 * q^50 - z^2 * q^51 + z^5 * q^54 + z^6 * q^56 - z^6 * q^63 - z * q^64 - z^4 * q^66 - z^4 * q^67 + z * q^72 - q^75 + z^5 * q^77 + z^4 * q^78 - z * q^81 - 2z^6 q^82 - q^88 + z^6 * q^89 - z^5 * q^91 + z^2 * q^94 + q^99
$\operatorname{Tr}(f)(q)$	$=$	$6 q - q^{2} + q^{3} + q^{6} + q^{7} + q^{8} - q^{9} - q^{11} + q^{13} + q^{14} + q^{16} + 6 q^{17} - q^{18} - q^{21} - q^{22} - q^{24} - q^{25} + q^{26} + q^{27} + q^{33} - q^{34} - q^{39}+ \cdots + 6 q^{99}+O(q^{100})$ 6 * q - q^2 + q^3 + q^6 + q^7 + q^8 - q^9 - q^11 + q^13 + q^14 + q^16 + 6 * q^17 - q^18 - q^21 - q^22 - q^24 - q^25 + q^26 + q^27 + q^33 - q^34 - q^39 - 12 * q^41 - q^42 - q^47 - q^48 - q^50 + q^51 + q^54 - q^56 + q^63 - q^64 + q^66 + q^67 + q^72 - 6 * q^75 + q^77 - q^78 - q^81 + 2 * q^82 - 6 * q^88 - q^89 - q^91 - q^94 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2523\mathbb{Z}\right)^\times$ .

$n$	$842$	$1684$
$\chi(n)$	$-1$	$\zeta_{14}^{5}$

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}

236.1

0.222521	+	0.974928i
0.222521	−	0.974928i
−0.623490	+	0.781831i
−0.623490	−	0.781831i
0.900969	+	0.433884i
0.900969	−	0.433884i

−0.222521

0.974928i

0.900969

−

0.433884i

0.222521

0.974928i

0.900969

−

0.433884i

−0.623490

0.781831i

0.623490

−

0.781831i

1037.1

−0.222521

−

0.974928i

0.900969

0.433884i

0.222521

−

0.974928i

0.900969

0.433884i

−0.623490

−

0.781831i

0.623490

0.781831i

1745.1

0.623490

0.781831i

0.222521

0.974928i

−0.623490

0.781831i

0.222521

0.974928i

0.900969

−

0.433884i

−0.900969

0.433884i

1949.1

0.623490

−

0.781831i

0.222521

−

0.974928i

−0.623490

−

0.781831i

0.222521

−

0.974928i

0.900969

0.433884i

−0.900969

−

0.433884i

1952.1

−0.900969

0.433884i

−0.623490

−

0.781831i

0.900969

0.433884i

−0.623490

−

0.781831i

0.222521

−

0.974928i

−0.222521

0.974928i

2333.1

−0.900969

−

0.433884i

−0.623490

0.781831i

0.900969

−

0.433884i

−0.623490

0.781831i

0.222521

0.974928i

−0.222521

−

0.974928i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
87.d	odd	2	1	CM by $\Q(\sqrt{-87})$
29.d	even	7	5	inner
87.h	odd	14	5	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2523.1.h.a		6
3.b	odd	2	1		2523.1.h.b		6
29.b	even	2	1		2523.1.h.b		6
29.c	odd	4	2		2523.1.j.b		12
29.d	even	7	1		87.1.d.b	yes	1
29.d	even	7	5	inner	2523.1.h.a		6
29.e	even	14	1		87.1.d.a	✓	1
29.e	even	14	5		2523.1.h.b		6
29.f	odd	28	2		2523.1.b.b		2
29.f	odd	28	10		2523.1.j.b		12
87.d	odd	2	1	CM	2523.1.h.a		6
87.f	even	4	2		2523.1.j.b		12
87.h	odd	14	1		87.1.d.b	yes	1
87.h	odd	14	5	inner	2523.1.h.a		6
87.j	odd	14	1		87.1.d.a	✓	1
87.j	odd	14	5		2523.1.h.b		6
87.k	even	28	2		2523.1.b.b		2
87.k	even	28	10		2523.1.j.b		12
116.h	odd	14	1		1392.1.i.a		1
116.j	odd	14	1		1392.1.i.b		1
145.l	even	14	1		2175.1.h.b		1
145.n	even	14	1		2175.1.h.a		1
145.p	odd	28	2		2175.1.b.b		2
145.q	odd	28	2		2175.1.b.a		2
261.q	even	21	2		2349.1.h.a		2
261.t	odd	42	2		2349.1.h.b		2
261.u	even	42	2		2349.1.h.b		2
261.v	odd	42	2		2349.1.h.a		2
348.s	even	14	1		1392.1.i.a		1
348.t	even	14	1		1392.1.i.b		1
435.w	odd	14	1		2175.1.h.b		1
435.bb	odd	14	1		2175.1.h.a		1
435.bg	even	28	2		2175.1.b.b		2
435.bj	even	28	2		2175.1.b.a		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
87.1.d.a	✓	1	29.e	even	14	1
87.1.d.a	✓	1	87.j	odd	14	1
87.1.d.b	yes	1	29.d	even	7	1
87.1.d.b	yes	1	87.h	odd	14	1
1392.1.i.a		1	116.h	odd	14	1
1392.1.i.a		1	348.s	even	14	1
1392.1.i.b		1	116.j	odd	14	1
1392.1.i.b		1	348.t	even	14	1
2175.1.b.a		2	145.q	odd	28	2
2175.1.b.a		2	435.bj	even	28	2
2175.1.b.b		2	145.p	odd	28	2
2175.1.b.b		2	435.bg	even	28	2
2175.1.h.a		1	145.n	even	14	1
2175.1.h.a		1	435.bb	odd	14	1
2175.1.h.b		1	145.l	even	14	1
2175.1.h.b		1	435.w	odd	14	1
2349.1.h.a		2	261.q	even	21	2
2349.1.h.a		2	261.v	odd	42	2
2349.1.h.b		2	261.t	odd	42	2
2349.1.h.b		2	261.u	even	42	2
2523.1.b.b		2	29.f	odd	28	2
2523.1.b.b		2	87.k	even	28	2
2523.1.h.a		6	1.a	even	1	1	trivial
2523.1.h.a		6	29.d	even	7	5	inner
2523.1.h.a		6	87.d	odd	2	1	CM
2523.1.h.a		6	87.h	odd	14	5	inner
2523.1.h.b		6	3.b	odd	2	1
2523.1.h.b		6	29.b	even	2	1
2523.1.h.b		6	29.e	even	14	5
2523.1.h.b		6	87.j	odd	14	5
2523.1.j.b		12	29.c	odd	4	2
2523.1.j.b		12	29.f	odd	28	10
2523.1.j.b		12	87.f	even	4	2
2523.1.j.b		12	87.k	even	28	10

This newform subspace can be constructed as the kernel of the linear operator $T_{2}^{6} + T_{2}^{5} + T_{2}^{4} + T_{2}^{3} + T_{2}^{2} + T_{2} + 1$ T2^6 + T2^5 + T2^4 + T2^3 + T2^2 + T2 + 1 acting on $S_{1}^{\mathrm{new}}(2523, [\chi])$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{6} + T^{5} + T^{4} + \cdots + 1$ T^6 + T^5 + T^4 + T^3 + T^2 + T + 1
$3$	$T^{6} - T^{5} + T^{4} + \cdots + 1$ T^6 - T^5 + T^4 - T^3 + T^2 - T + 1
$5$	$T^{6}$ T^6
$7$	$T^{6} - T^{5} + T^{4} + \cdots + 1$ T^6 - T^5 + T^4 - T^3 + T^2 - T + 1
$11$	$T^{6} + T^{5} + T^{4} + \cdots + 1$ T^6 + T^5 + T^4 + T^3 + T^2 + T + 1
$13$	$T^{6} - T^{5} + T^{4} + \cdots + 1$ T^6 - T^5 + T^4 - T^3 + T^2 - T + 1
$17$	$(T - 1)^{6}$ (T - 1)^6
$19$	$T^{6}$ T^6
$23$	$T^{6}$ T^6
$29$	$T^{6}$ T^6
$31$	$T^{6}$ T^6
$37$	$T^{6}$ T^6
$41$	$(T + 2)^{6}$ (T + 2)^6
$43$	$T^{6}$ T^6
$47$	$T^{6} + T^{5} + T^{4} + \cdots + 1$ T^6 + T^5 + T^4 + T^3 + T^2 + T + 1
$53$	$T^{6}$ T^6
$59$	$T^{6}$ T^6
$61$	$T^{6}$ T^6
$67$	$T^{6} - T^{5} + T^{4} + \cdots + 1$ T^6 - T^5 + T^4 - T^3 + T^2 - T + 1
$71$	$T^{6}$ T^6
$73$	$T^{6}$ T^6
$79$	$T^{6}$ T^6
$83$	$T^{6}$ T^6
$89$	$T^{6} + T^{5} + T^{4} + \cdots + 1$ T^6 + T^5 + T^4 + T^3 + T^2 + T + 1
$97$	$T^{6}$ T^6
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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 $\F_{q}$

$n$ :		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 236.1
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Database

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Newspace parameters

Newform invariants

$q$ -expansion

Character values

Embeddings

Inner twists

Twists

Hecke kernels

Hecke characteristic polynomials

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	2523.1.h.a

Level	$2523$
Weight	$1$
Character orbit	2523.h
Analytic conductor	$1.259$
Analytic rank	$0$
Dimension	$6$
Projective image	$D_{3}$
CM discriminant	-87
Inner twists	$12$