LMFDB - Newform orbit 525.4.a.g

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.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:	$30.9760027530$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
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 + 3 q^{2} + 3 q^{3} + q^{4} + 9 q^{6} - 7 q^{7} - 21 q^{8} + 9 q^{9}+O(q^{10}) $

$ q + 3 q^{2} + 3 q^{3} + q^{4} + 9 q^{6} - 7 q^{7} - 21 q^{8} + 9 q^{9} - 36 q^{11} + 3 q^{12} + 34 q^{13} - 21 q^{14} - 71 q^{16} - 42 q^{17} + 27 q^{18} - 124 q^{19} - 21 q^{21} - 108 q^{22} - 63 q^{24} + 102 q^{26} + 27 q^{27} - 7 q^{28} + 102 q^{29} - 160 q^{31} - 45 q^{32} - 108 q^{33} - 126 q^{34} + 9 q^{36} - 398 q^{37} - 372 q^{38} + 102 q^{39} - 318 q^{41} - 63 q^{42} + 268 q^{43} - 36 q^{44} - 240 q^{47} - 213 q^{48} + 49 q^{49} - 126 q^{51} + 34 q^{52} + 498 q^{53} + 81 q^{54} + 147 q^{56} - 372 q^{57} + 306 q^{58} - 132 q^{59} + 398 q^{61} - 480 q^{62} - 63 q^{63} + 433 q^{64} - 324 q^{66} - 92 q^{67} - 42 q^{68} - 720 q^{71} - 189 q^{72} + 502 q^{73} - 1194 q^{74} - 124 q^{76} + 252 q^{77} + 306 q^{78} - 1024 q^{79} + 81 q^{81} - 954 q^{82} + 204 q^{83} - 21 q^{84} + 804 q^{86} + 306 q^{87} + 756 q^{88} + 354 q^{89} - 238 q^{91} - 480 q^{93} - 720 q^{94} - 135 q^{96} + 286 q^{97} + 147 q^{98} - 324 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

3.00000

1.00000

9.00000

−7.00000

−21.0000

9.00000

Atkin-Lehner signs

$ p $	Sign
$3$	$-1$
$5$	$1$
$7$	$1$

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	525.4.a.g		1
3.b	odd	2	1		1575.4.a.b		1
5.b	even	2	1		21.4.a.a	✓	1
5.c	odd	4	2		525.4.d.c		2
15.d	odd	2	1		63.4.a.c		1
20.d	odd	2	1		336.4.a.f		1
35.c	odd	2	1		147.4.a.c		1
35.i	odd	6	2		147.4.e.g		2
35.j	even	6	2		147.4.e.i		2
40.e	odd	2	1		1344.4.a.n		1
40.f	even	2	1		1344.4.a.ba		1
60.h	even	2	1		1008.4.a.v		1
105.g	even	2	1		441.4.a.j		1
105.o	odd	6	2		441.4.e.b		2
105.p	even	6	2		441.4.e.d		2
140.c	even	2	1		2352.4.a.r		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
21.4.a.a	✓	1	5.b	even	2	1
63.4.a.c		1	15.d	odd	2	1
147.4.a.c		1	35.c	odd	2	1
147.4.e.g		2	35.i	odd	6	2
147.4.e.i		2	35.j	even	6	2
336.4.a.f		1	20.d	odd	2	1
441.4.a.j		1	105.g	even	2	1
441.4.e.b		2	105.o	odd	6	2
441.4.e.d		2	105.p	even	6	2
525.4.a.g		1	1.a	even	1	1	trivial
525.4.d.c		2	5.c	odd	4	2
1008.4.a.v		1	60.h	even	2	1
1344.4.a.n		1	40.e	odd	2	1
1344.4.a.ba		1	40.f	even	2	1
1575.4.a.b		1	3.b	odd	2	1
2352.4.a.r		1	140.c	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(525))$:

$ T_{2} - 3 $

$ T_{11} + 36 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 3 $ T - 3
$3$	$ T - 3 $ T - 3
$5$	$ T $ T
$7$	$ T + 7 $ T + 7
$11$	$ T + 36 $ T + 36
$13$	$ T - 34 $ T - 34
$17$	$ T + 42 $ T + 42
$19$	$ T + 124 $ T + 124
$23$	$ T $ T
$29$	$ T - 102 $ T - 102
$31$	$ T + 160 $ T + 160
$37$	$ T + 398 $ T + 398
$41$	$ T + 318 $ T + 318
$43$	$ T - 268 $ T - 268
$47$	$ T + 240 $ T + 240
$53$	$ T - 498 $ T - 498
$59$	$ T + 132 $ T + 132
$61$	$ T - 398 $ T - 398
$67$	$ T + 92 $ T + 92
$71$	$ T + 720 $ T + 720
$73$	$ T - 502 $ T - 502
$79$	$ T + 1024 $ T + 1024
$83$	$ T - 204 $ T - 204
$89$	$ T - 354 $ T - 354
$97$	$ T - 286 $ T - 286
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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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

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