LMFDB - Newform orbit 24.3.h.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,3,Mod(5,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("24.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	24.h (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:	$0.653952634465$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
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 - 2 q^{2} + 3 q^{3} + 4 q^{4} + 2 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} + 9 q^{9}+O(q^{10}) $

$ q - 2 q^{2} + 3 q^{3} + 4 q^{4} + 2 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} + 9 q^{9} - 4 q^{10} - 10 q^{11} + 12 q^{12} + 20 q^{14} + 6 q^{15} + 16 q^{16} - 18 q^{18} + 8 q^{20} - 30 q^{21} + 20 q^{22} - 24 q^{24} - 21 q^{25} + 27 q^{27} - 40 q^{28} + 50 q^{29} - 12 q^{30} + 38 q^{31} - 32 q^{32} - 30 q^{33} - 20 q^{35} + 36 q^{36} - 16 q^{40} + 60 q^{42} - 40 q^{44} + 18 q^{45} + 48 q^{48} + 51 q^{49} + 42 q^{50} - 94 q^{53} - 54 q^{54} - 20 q^{55} + 80 q^{56} - 100 q^{58} - 10 q^{59} + 24 q^{60} - 76 q^{62} - 90 q^{63} + 64 q^{64} + 60 q^{66} + 40 q^{70} - 72 q^{72} + 50 q^{73} - 63 q^{75} + 100 q^{77} - 58 q^{79} + 32 q^{80} + 81 q^{81} + 134 q^{83} - 120 q^{84} + 150 q^{87} + 80 q^{88} - 36 q^{90} + 114 q^{93} - 96 q^{96} - 190 q^{97} - 102 q^{98} - 90 q^{99}+O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$1$	$-1$	$-1$

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} $

5.1

−2.00000

3.00000

4.00000

2.00000

−6.00000

−10.0000

−8.00000

9.00000

−4.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
24.h	odd	2	1	CM by $\Q(\sqrt{-6}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	24.3.h.a	✓	1
3.b	odd	2	1		24.3.h.b	yes	1
4.b	odd	2	1		96.3.h.a		1
8.b	even	2	1		24.3.h.b	yes	1
8.d	odd	2	1		96.3.h.b		1
12.b	even	2	1		96.3.h.b		1
16.e	even	4	2		768.3.e.d		2
16.f	odd	4	2		768.3.e.c		2
24.f	even	2	1		96.3.h.a		1
24.h	odd	2	1	CM	24.3.h.a	✓	1
48.i	odd	4	2		768.3.e.d		2
48.k	even	4	2		768.3.e.c		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
24.3.h.a	✓	1	1.a	even	1	1	trivial
24.3.h.a	✓	1	24.h	odd	2	1	CM
24.3.h.b	yes	1	3.b	odd	2	1
24.3.h.b	yes	1	8.b	even	2	1
96.3.h.a		1	4.b	odd	2	1
96.3.h.a		1	24.f	even	2	1
96.3.h.b		1	8.d	odd	2	1
96.3.h.b		1	12.b	even	2	1
768.3.e.c		2	16.f	odd	4	2
768.3.e.c		2	48.k	even	4	2
768.3.e.d		2	16.e	even	4	2
768.3.e.d		2	48.i	odd	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{5} - 2 $ T5 - 2 acting on $S_{3}^{\mathrm{new}}(24, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 2 $ T + 2
$3$	$ T - 3 $ T - 3
$5$	$ T - 2 $ T - 2
$7$	$ T + 10 $ T + 10
$11$	$ T + 10 $ T + 10
$13$	$ T $ T
$17$	$ T $ T
$19$	$ T $ T
$23$	$ T $ T
$29$	$ T - 50 $ T - 50
$31$	$ T - 38 $ T - 38
$37$	$ T $ T
$41$	$ T $ T
$43$	$ T $ T
$47$	$ T $ T
$53$	$ T + 94 $ T + 94
$59$	$ T + 10 $ T + 10
$61$	$ T $ T
$67$	$ T $ T
$71$	$ T $ T
$73$	$ T - 50 $ T - 50
$79$	$ T + 58 $ T + 58
$83$	$ T - 134 $ T - 134
$89$	$ T $ T
$97$	$ T + 190 $ T + 190
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Elliptic curves over $\Q$
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Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	24.h (of order \(2\), degree \(1\), minimal)

\(n\)	\(7\)	\(13\)	\(17\)
\(\chi(n)\)	\(1\)	\(-1\)	\(-1\)

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