LMFDB - Newform orbit 24.21.h.a

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [24,21,Mod(5,24)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("24.5"); S:= CuspForms(chi, 21); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(24, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 21, names="a")

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	24.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [1,-1024] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$60.8433036246$
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 - 1024 q^{2} - 59049 q^{3} + 1048576 q^{4} - 8368274 q^{5} + 60466176 q^{6} + 57552002 q^{7} - 1073741824 q^{8} + 3486784401 q^{9} + 8569112576 q^{10} + 323146702 q^{11} - 61917364224 q^{12} - 58933250048 q^{14}+ \cdots + 11\!\cdots\!02 q^{99}+O(q^{100}) $

q - 1024 * q^2 - 59049 * q^3 + 1048576 * q^4 - 8368274 * q^5 + 60466176 * q^6 + 57552002 * q^7 - 1073741824 * q^8 + 3486784401 * q^9 + 8569112576 * q^10 + 323146702 * q^11 - 61917364224 * q^12 - 58933250048 * q^14 + 494138211426 * q^15 + 1099511627776 * q^16 - 3570467226624 * q^18 - 8774771277824 * q^20 - 3398388166098 * q^21 - 330902222848 * q^22 + 63403380965376 * q^24 - 25339421901549 * q^25 - 205891132094649 * q^27 + 60347648049152 * q^28 - 476620405962098 * q^29 - 505997528500224 * q^30 - 1559050184498398 * q^31 - 1125899906842624 * q^32 - 19081489606398 * q^33 - 481610921984548 * q^35 + 3656158440062976 * q^36 + 8985365788491776 * q^40 + 3479949482084352 * q^42 + 338843876196352 * q^44 - 29178367246493874 * q^45 - 64925062108545024 * q^48 - 76480033363403997 * q^49 + 25947568027186176 * q^50 - 32131738161366098 * q^53 + 210832519264920576 * q^54 - 2704180144532348 * q^55 - 61795991602331648 * q^56 + 488059295705188352 * q^58 + 675827042775980302 * q^59 + 518141469184229376 * q^60 + 1596467388926359552 * q^62 + 200671422819920802 * q^63 + 1152921504606846976 * q^64 + 19539445356951552 * q^66 + 493169584112177152 * q^70 - 3743906242624487424 * q^72 + 8062862040535447202 * q^73 + 1496267523864566901 * q^75 + 18597739639797404 * q^77 + 15443028157438754402 * q^79 - 9201014567415578624 * q^80 + 12157665459056928801 * q^81 - 31017784480433866898 * q^83 - 3563468269654376448 * q^84 + 28143958351655924802 * q^87 - 346976129225064448 * q^88 + 29878648060409726976 * q^90 + 92060354344445903502 * q^93 + 66483263599150104576 * q^96 - 65924745434247849598 * q^97 + 78315554164125692928 * q^98 + 1126742879768195502 * q^99

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

−1024.00

−59049.0

1.04858e6

−8.36827e6

6.04662e7

5.75520e7

−1.07374e9

3.48678e9

8.56911e9

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	24.21.h.a	✓	1
3.b	odd	2	1		24.21.h.b	yes	1
8.b	even	2	1		24.21.h.b	yes	1
24.h	odd	2	1	CM	24.21.h.a	✓	1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
24.21.h.a	✓	1	1.a	even	1	1	trivial
24.21.h.a	✓	1	24.h	odd	2	1	CM
24.21.h.b	yes	1	3.b	odd	2	1
24.21.h.b	yes	1	8.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{5} + 8368274 $ T5 + 8368274 acting on $S_{21}^{\mathrm{new}}(24, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 1024 $ T + 1024
$3$	$ T + 59049 $ T + 59049
$5$	$ T + 8368274 $ T + 8368274
$7$	$ T - 57552002 $ T - 57552002
$11$	$ T - 323146702 $ T - 323146702
$13$	$ T $ T
$17$	$ T $ T
$19$	$ T $ T
$23$	$ T $ T
$29$	$ T + 476620405962098 $ T + 476620405962098
$31$	$ T + 1559050184498398 $ T + 1559050184498398
$37$	$ T $ T
$41$	$ T $ T
$43$	$ T $ T
$47$	$ T $ T
$53$	$ T + 32\!\cdots\!98 $ T + 32131738161366098
$59$	$ T - 67\!\cdots\!02 $ T - 675827042775980302
$61$	$ T $ T
$67$	$ T $ T
$71$	$ T $ T
$73$	$ T - 80\!\cdots\!02 $ T - 8062862040535447202
$79$	$ T - 15\!\cdots\!02 $ T - 15443028157438754402
$83$	$ T + 31\!\cdots\!98 $ T + 31017784480433866898
$89$	$ T $ T
$97$	$ T + 65\!\cdots\!98 $ T + 65924745434247849598
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Elliptic curves over $\Q$
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Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	24.h (of order \(2\), degree \(1\), minimal)

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

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