LMFDB - Newform orbit 2475.4.a.j

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2475,4,Mod(1,2475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2475, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2475.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 2475 = 3^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2475.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,4,0,8,0,0,21,0,0,0,-11] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$146.029727264$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 825)
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 + 4 q^{2} + 8 q^{4} + 21 q^{7} - 11 q^{11} - 68 q^{13} + 84 q^{14} - 64 q^{16} - 21 q^{17} + 125 q^{19} - 44 q^{22} - 137 q^{23} - 272 q^{26} + 168 q^{28} + 150 q^{29} + 292 q^{31} - 256 q^{32} - 84 q^{34}+ \cdots + 392 q^{98}+O(q^{100}) $

q + 4 * q^2 + 8 * q^4 + 21 * q^7 - 11 * q^11 - 68 * q^13 + 84 * q^14 - 64 * q^16 - 21 * q^17 + 125 * q^19 - 44 * q^22 - 137 * q^23 - 272 * q^26 + 168 * q^28 + 150 * q^29 + 292 * q^31 - 256 * q^32 - 84 * q^34 - 349 * q^37 + 500 * q^38 - 497 * q^41 - 208 * q^43 - 88 * q^44 - 548 * q^46 + 369 * q^47 + 98 * q^49 - 544 * q^52 - 542 * q^53 + 600 * q^58 - 235 * q^59 + 482 * q^61 + 1168 * q^62 - 512 * q^64 - 734 * q^67 - 168 * q^68 - 587 * q^71 - 518 * q^73 - 1396 * q^74 + 1000 * q^76 - 231 * q^77 - 1045 * q^79 - 1988 * q^82 + 608 * q^83 - 832 * q^86 + 770 * q^89 - 1428 * q^91 - 1096 * q^92 + 1476 * q^94 + 1541 * q^97 + 392 * q^98

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

4.00000

8.00000

21.0000

Atkin-Lehner signs

$ p $	Sign
$3$	$ -1 $
$5$	$ +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	2475.4.a.j		1
3.b	odd	2	1		825.4.a.b	✓	1
5.b	even	2	1		2475.4.a.c		1
15.d	odd	2	1		825.4.a.h	yes	1
15.e	even	4	2		825.4.c.c		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
825.4.a.b	✓	1	3.b	odd	2	1
825.4.a.h	yes	1	15.d	odd	2	1
825.4.c.c		2	15.e	even	4	2
2475.4.a.c		1	5.b	even	2	1
2475.4.a.j		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(2475))$:

$ T_{2} - 4 $

T2 - 4

$ T_{7} - 21 $

T7 - 21

$ T_{29} - 150 $

T29 - 150

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 4 $ T - 4
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T - 21 $ T - 21
$11$	$ T + 11 $ T + 11
$13$	$ T + 68 $ T + 68
$17$	$ T + 21 $ T + 21
$19$	$ T - 125 $ T - 125
$23$	$ T + 137 $ T + 137
$29$	$ T - 150 $ T - 150
$31$	$ T - 292 $ T - 292
$37$	$ T + 349 $ T + 349
$41$	$ T + 497 $ T + 497
$43$	$ T + 208 $ T + 208
$47$	$ T - 369 $ T - 369
$53$	$ T + 542 $ T + 542
$59$	$ T + 235 $ T + 235
$61$	$ T - 482 $ T - 482
$67$	$ T + 734 $ T + 734
$71$	$ T + 587 $ T + 587
$73$	$ T + 518 $ T + 518
$79$	$ T + 1045 $ T + 1045
$83$	$ T - 608 $ T - 608
$89$	$ T - 770 $ T - 770
$97$	$ T - 1541 $ T - 1541
show more
show less

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2475.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
Format:

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more