LMFDB - Newform orbit 25.4.a.c

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.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:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 5)
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} - 2 q^{3} + 8 q^{4} - 8 q^{6} - 6 q^{7} - 23 q^{9}+O(q^{10}) $

$ q + 4 q^{2} - 2 q^{3} + 8 q^{4} - 8 q^{6} - 6 q^{7} - 23 q^{9} + 32 q^{11} - 16 q^{12} + 38 q^{13} - 24 q^{14} - 64 q^{16} - 26 q^{17} - 92 q^{18} + 100 q^{19} + 12 q^{21} + 128 q^{22} + 78 q^{23} + 152 q^{26} + 100 q^{27} - 48 q^{28} - 50 q^{29} - 108 q^{31} - 256 q^{32} - 64 q^{33} - 104 q^{34} - 184 q^{36} - 266 q^{37} + 400 q^{38} - 76 q^{39} + 22 q^{41} + 48 q^{42} - 442 q^{43} + 256 q^{44} + 312 q^{46} + 514 q^{47} + 128 q^{48} - 307 q^{49} + 52 q^{51} + 304 q^{52} - 2 q^{53} + 400 q^{54} - 200 q^{57} - 200 q^{58} + 500 q^{59} - 518 q^{61} - 432 q^{62} + 138 q^{63} - 512 q^{64} - 256 q^{66} - 126 q^{67} - 208 q^{68} - 156 q^{69} + 412 q^{71} + 878 q^{73} - 1064 q^{74} + 800 q^{76} - 192 q^{77} - 304 q^{78} + 600 q^{79} + 421 q^{81} + 88 q^{82} - 282 q^{83} + 96 q^{84} - 1768 q^{86} + 100 q^{87} - 150 q^{89} - 228 q^{91} + 624 q^{92} + 216 q^{93} + 2056 q^{94} + 512 q^{96} - 386 q^{97} - 1228 q^{98} - 736 q^{99}+O(q^{100}) $

Display 100 coefficients 10 coefficients

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

−2.00000

8.00000

−8.00000

−6.00000

−23.0000

Atkin-Lehner signs

$ p $	Sign
$5$	$1$

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	25.4.a.c		1
3.b	odd	2	1		225.4.a.b		1
4.b	odd	2	1		400.4.a.m		1
5.b	even	2	1		5.4.a.a	✓	1
5.c	odd	4	2		25.4.b.a		2
7.b	odd	2	1		1225.4.a.k		1
8.b	even	2	1		1600.4.a.bi		1
8.d	odd	2	1		1600.4.a.s		1
15.d	odd	2	1		45.4.a.d		1
15.e	even	4	2		225.4.b.c		2
20.d	odd	2	1		80.4.a.d		1
20.e	even	4	2		400.4.c.k		2
35.c	odd	2	1		245.4.a.a		1
35.i	odd	6	2		245.4.e.g		2
35.j	even	6	2		245.4.e.f		2
40.e	odd	2	1		320.4.a.h		1
40.f	even	2	1		320.4.a.g		1
45.h	odd	6	2		405.4.e.c		2
45.j	even	6	2		405.4.e.l		2
55.d	odd	2	1		605.4.a.d		1
60.h	even	2	1		720.4.a.u		1
65.d	even	2	1		845.4.a.b		1
80.k	odd	4	2		1280.4.d.l		2
80.q	even	4	2		1280.4.d.e		2
85.c	even	2	1		1445.4.a.a		1
95.d	odd	2	1		1805.4.a.h		1
105.g	even	2	1		2205.4.a.q		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
5.4.a.a	✓	1	5.b	even	2	1
25.4.a.c		1	1.a	even	1	1	trivial
25.4.b.a		2	5.c	odd	4	2
45.4.a.d		1	15.d	odd	2	1
80.4.a.d		1	20.d	odd	2	1
225.4.a.b		1	3.b	odd	2	1
225.4.b.c		2	15.e	even	4	2
245.4.a.a		1	35.c	odd	2	1
245.4.e.f		2	35.j	even	6	2
245.4.e.g		2	35.i	odd	6	2
320.4.a.g		1	40.f	even	2	1
320.4.a.h		1	40.e	odd	2	1
400.4.a.m		1	4.b	odd	2	1
400.4.c.k		2	20.e	even	4	2
405.4.e.c		2	45.h	odd	6	2
405.4.e.l		2	45.j	even	6	2
605.4.a.d		1	55.d	odd	2	1
720.4.a.u		1	60.h	even	2	1
845.4.a.b		1	65.d	even	2	1
1225.4.a.k		1	7.b	odd	2	1
1280.4.d.e		2	80.q	even	4	2
1280.4.d.l		2	80.k	odd	4	2
1445.4.a.a		1	85.c	even	2	1
1600.4.a.s		1	8.d	odd	2	1
1600.4.a.bi		1	8.b	even	2	1
1805.4.a.h		1	95.d	odd	2	1
2205.4.a.q		1	105.g	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{2} - 4 $ T2 - 4 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(25))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 4 $ T - 4
$3$	$ T + 2 $ T + 2
$5$	$ T $ T
$7$	$ T + 6 $ T + 6
$11$	$ T - 32 $ T - 32
$13$	$ T - 38 $ T - 38
$17$	$ T + 26 $ T + 26
$19$	$ T - 100 $ T - 100
$23$	$ T - 78 $ T - 78
$29$	$ T + 50 $ T + 50
$31$	$ T + 108 $ T + 108
$37$	$ T + 266 $ T + 266
$41$	$ T - 22 $ T - 22
$43$	$ T + 442 $ T + 442
$47$	$ T - 514 $ T - 514
$53$	$ T + 2 $ T + 2
$59$	$ T - 500 $ T - 500
$61$	$ T + 518 $ T + 518
$67$	$ T + 126 $ T + 126
$71$	$ T - 412 $ T - 412
$73$	$ T - 878 $ T - 878
$79$	$ T - 600 $ T - 600
$83$	$ T + 282 $ T + 282
$89$	$ T + 150 $ T + 150
$97$	$ T + 386 $ T + 386
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Overview	Random
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Classical	Maass
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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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

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