LMFDB - Newform orbit 726.2.i.c

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(67,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 20])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,-6] 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:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) = $ $ 60 q - 6 q^{2} - 60 q^{3} - 6 q^{4} - 2 q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 60 q^{9} - 13 q^{10} - 10 q^{11} + 6 q^{12} - 17 q^{13} - 6 q^{14} + 2 q^{15} - 6 q^{16} + 10 q^{17} - 6 q^{18} - 4 q^{19} - 2 q^{20}+ \cdots - 10 q^{99}+O(q^{100}) $

60 * q - 6 * q^2 - 60 * q^3 - 6 * q^4 - 2 * q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 60 * q^9 - 13 * q^10 - 10 * q^11 + 6 * q^12 - 17 * q^13 - 6 * q^14 + 2 * q^15 - 6 * q^16 + 10 * q^17 - 6 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 10 * q^22 - 26 * q^23 + 6 * q^24 - 2 * q^25 + 5 * q^26 - 60 * q^27 + 5 * q^28 - 6 * q^29 + 13 * q^30 - 52 * q^31 - 6 * q^32 + 10 * q^33 + 10 * q^34 + 63 * q^35 - 6 * q^36 - 47 * q^37 + 18 * q^38 + 17 * q^39 - 2 * q^40 + 27 * q^41 + 6 * q^42 + 84 * q^43 + q^44 - 2 * q^45 + 7 * q^46 + 10 * q^47 + 6 * q^48 - 33 * q^49 - 2 * q^50 - 10 * q^51 + 5 * q^52 + 42 * q^53 + 6 * q^54 + 13 * q^55 - 6 * q^56 + 4 * q^57 + 16 * q^58 - 11 * q^59 + 2 * q^60 - 24 * q^61 + 14 * q^62 + 5 * q^63 - 6 * q^64 - 80 * q^65 + 10 * q^66 - 2 * q^67 - q^68 + 26 * q^69 - 14 * q^70 - 30 * q^71 - 6 * q^72 - 51 * q^73 + 8 * q^74 + 2 * q^75 - 4 * q^76 + 73 * q^77 - 5 * q^78 - 30 * q^79 - 2 * q^80 + 60 * q^81 - 6 * q^82 + 4 * q^83 - 5 * q^84 + 45 * q^85 - 4 * q^86 + 6 * q^87 + 12 * q^88 - 44 * q^89 - 13 * q^90 - 90 * q^91 + 7 * q^92 + 52 * q^93 - 78 * q^94 - 65 * q^95 + 6 * q^96 - 41 * q^97 + 33 * q^98 - 10 * q^99

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	$ a_{2} $			$ a_{3} $	$ a_{4} $			$ a_{5} $			$ a_{6} $			$ a_{7} $			$ a_{8} $			$ a_{9} $	$ a_{10} $
67.1	−0.959493	+	0.281733i	−1.00000	0.841254	−	0.540641i	−2.56949	−	2.96535i	0.959493	−	0.281733i	1.95930	+	4.29026i	−0.654861	+	0.755750i	1.00000	3.30085	+	2.12132i
67.2	−0.959493	+	0.281733i	−1.00000	0.841254	−	0.540641i	−0.806572	−	0.930834i	0.959493	−	0.281733i	−0.184135	−	0.403198i	−0.654861	+	0.755750i	1.00000	1.03615	+	0.665891i
67.3	−0.959493	+	0.281733i	−1.00000	0.841254	−	0.540641i	−0.0837911	−	0.0967001i	0.959493	−	0.281733i	−0.653344	−	1.43062i	−0.654861	+	0.755750i	1.00000	0.107641	+	0.0691764i
67.4	−0.959493	+	0.281733i	−1.00000	0.841254	−	0.540641i	0.727009	+	0.839013i	0.959493	−	0.281733i	0.246193	+	0.539087i	−0.654861	+	0.755750i	1.00000	−0.933937	−	0.600205i
67.5	−0.959493	+	0.281733i	−1.00000	0.841254	−	0.540641i	1.77550	+	2.04904i	0.959493	−	0.281733i	2.17193	+	4.75586i	−0.654861	+	0.755750i	1.00000	−2.28087	−	1.46582i
67.6	−0.959493	+	0.281733i	−1.00000	0.841254	−	0.540641i	2.43194	+	2.80660i	0.959493	−	0.281733i	−1.66503	−	3.64591i	−0.654861	+	0.755750i	1.00000	−3.12414	−	2.00776i
133.1	0.841254	−	0.540641i	−1.00000	0.415415	−	0.909632i	−0.196232	+	1.36482i	−0.841254	+	0.540641i	2.02489	−	2.33685i	−0.142315	−	0.989821i	1.00000	0.572797	+	1.25425i
133.2	0.841254	−	0.540641i	−1.00000	0.415415	−	0.909632i	−0.186845	+	1.29954i	−0.841254	+	0.540641i	−0.229226	+	0.264540i	−0.142315	−	0.989821i	1.00000	0.545399	+	1.19426i
133.3	0.841254	−	0.540641i	−1.00000	0.415415	−	0.909632i	−0.149872	+	1.04238i	−0.841254	+	0.540641i	−1.49653	+	1.72708i	−0.142315	−	0.989821i	1.00000	0.437474	+	0.957934i
133.4	0.841254	−	0.540641i	−1.00000	0.415415	−	0.909632i	0.245189	−	1.70533i	−0.841254	+	0.540641i	−0.219849	+	0.253720i	−0.142315	−	0.989821i	1.00000	−0.715703	−	1.56717i
133.5	0.841254	−	0.540641i	−1.00000	0.415415	−	0.909632i	0.349688	−	2.43213i	−0.841254	+	0.540641i	−3.14342	+	3.62770i	−0.142315	−	0.989821i	1.00000	−1.02073	−	2.23510i
133.6	0.841254	−	0.540641i	−1.00000	0.415415	−	0.909632i	0.602512	−	4.19056i	−0.841254	+	0.540641i	2.06802	−	2.38662i	−0.142315	−	0.989821i	1.00000	−1.75872	−	3.85107i
199.1	−0.654861	+	0.755750i	−1.00000	−0.142315	−	0.989821i	−3.38359	+	2.17450i	0.654861	−	0.755750i	0.0704423	+	0.0206837i	0.841254	+	0.540641i	1.00000	0.572402	−	3.98114i
199.2	−0.654861	+	0.755750i	−1.00000	−0.142315	−	0.989821i	−0.915370	+	0.588273i	0.654861	−	0.755750i	−4.12515	−	1.21125i	0.841254	+	0.540641i	1.00000	0.154853	−	1.07703i
199.3	−0.654861	+	0.755750i	−1.00000	−0.142315	−	0.989821i	0.650217	−	0.417869i	0.654861	−	0.755750i	3.42744	+	1.00639i	0.841254	+	0.540641i	1.00000	−0.109997	+	0.765047i
199.4	−0.654861	+	0.755750i	−1.00000	−0.142315	−	0.989821i	0.679842	−	0.436908i	0.654861	−	0.755750i	−0.703516	−	0.206571i	0.841254	+	0.540641i	1.00000	−0.115009	+	0.799904i
199.5	−0.654861	+	0.755750i	−1.00000	−0.142315	−	0.989821i	0.886906	−	0.569980i	0.654861	−	0.755750i	−1.75005	−	0.513861i	0.841254	+	0.540641i	1.00000	−0.150038	+	1.04354i
199.6	−0.654861	+	0.755750i	−1.00000	−0.142315	−	0.989821i	3.71932	−	2.39026i	0.654861	−	0.755750i	3.27620	+	0.961980i	0.841254	+	0.540641i	1.00000	−0.629197	+	4.37616i
265.1	0.415415	−	0.909632i	−1.00000	−0.654861	−	0.755750i	−3.97541	−	1.16728i	−0.415415	+	0.909632i	0.122923	+	0.854951i	−0.959493	+	0.281733i	1.00000	−2.71324	+	3.13125i
265.2	0.415415	−	0.909632i	−1.00000	−0.654861	−	0.755750i	−3.41436	−	1.00255i	−0.415415	+	0.909632i	−0.408001	−	2.83771i	−0.959493	+	0.281733i	1.00000	−2.33032	+	2.68934i

See all 60 embeddings

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
121.e	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	726.2.i.c	✓	60
121.e	even	11	1	inner	726.2.i.c	✓	60

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
726.2.i.c	✓	60	1.a	even	1	1	trivial
726.2.i.c	✓	60	121.e	even	11	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{5}^{60} + 2 T_{5}^{59} + 18 T_{5}^{58} + 93 T_{5}^{57} + 503 T_{5}^{56} + 1766 T_{5}^{55} + \cdots + 52548001 $ T5^60 + 2*T5^59 + 18*T5^58 + 93*T5^57 + 503*T5^56 + 1766*T5^55 + 10251*T5^54 + 44910*T5^53 + 216657*T5^52 + 639491*T5^51 + 3303375*T5^50 + 10367916*T5^49 + 35452720*T5^48 + 54132321*T5^47 + 413374195*T5^46 + 541367655*T5^45 + 1775451755*T5^44 - 6727965787*T5^43 + 38297717400*T5^42 - 34345474054*T5^41 + 249787555407*T5^40 + 391824222671*T5^39 + 1518905864684*T5^38 + 3514218358826*T5^37 + 33928401524116*T5^36 - 97301263348494*T5^35 + 678606034286174*T5^34 - 1938500569294285*T5^33 + 5863938286488619*T5^32 - 12960223683883431*T5^31 + 26843772010691051*T5^30 - 47256019243526424*T5^29 + 77757110202360989*T5^28 - 115106485758963873*T5^27 + 162057598006305117*T5^26 - 212366022287767232*T5^25 + 266558007475701684*T5^24 - 315510120151237310*T5^23 + 358611899543518961*T5^22 - 387122038218376352*T5^21 + 403805597850540843*T5^20 - 405951692940801876*T5^19 + 396403271334492664*T5^18 - 369572626600032240*T5^17 + 324284443790386255*T5^16 - 259534295432415454*T5^15 + 184539735492442275*T5^14 - 111899994043896311*T5^13 + 55558437538597103*T5^12 - 20930118216158701*T5^11 + 5195418664997242*T5^10 - 349961433674347*T5^9 - 255396518089251*T5^8 + 93184082635215*T5^7 + 194851922991*T5^6 - 3760637952863*T5^5 + 252312920266*T5^4 + 31520739217*T5^3 + 3472194220*T5^2 - 1086523614*T5 + 52548001 acting on $S_{2}^{\mathrm{new}}(726, [\chi])$.

Overview	Random
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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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.i (of order \(11\), degree \(10\), minimal)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 67.6
Significant digits:
Format:

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