LMFDB - Newform orbit 798.2.cj.b

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(241,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.241"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cj (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

$\operatorname{Tr}(f)(q) = $ $ 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $

84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * 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} $
241.1	−0.342020	+	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	−2.65126	−	3.15965i	−0.342020	−	0.939693i	−2.64400	−	0.0962613i	0.866025	−	0.500000i	0.173648	−	0.984808i	3.87588	−	1.41071i
241.2	−0.342020	+	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	−1.14708	−	1.36703i	−0.342020	−	0.939693i	2.30387	+	1.30084i	0.866025	−	0.500000i	0.173648	−	0.984808i	1.67691	−	0.610346i
241.3	−0.342020	+	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	−0.687355	−	0.819158i	−0.342020	−	0.939693i	−1.68696	+	2.03818i	0.866025	−	0.500000i	0.173648	−	0.984808i	1.00485	−	0.365734i
241.4	−0.342020	+	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	0.363191	+	0.432835i	−0.342020	−	0.939693i	1.43186	−	2.22481i	0.866025	−	0.500000i	0.173648	−	0.984808i	−0.530950	+	0.193250i
241.5	−0.342020	+	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	0.860786	+	1.02584i	−0.342020	−	0.939693i	0.326418	+	2.62554i	0.866025	−	0.500000i	0.173648	−	0.984808i	−1.25838	+	0.458014i
241.6	−0.342020	+	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	1.19350	+	1.42236i	−0.342020	−	0.939693i	−1.25603	−	2.32860i	0.866025	−	0.500000i	0.173648	−	0.984808i	−1.74479	+	0.635050i
241.7	−0.342020	+	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	2.16291	+	2.57766i	−0.342020	−	0.939693i	−2.63218	+	0.267601i	0.866025	−	0.500000i	0.173648	−	0.984808i	−3.16197	+	1.15086i
241.8	0.342020	−	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	−2.62033	−	3.12278i	0.342020	+	0.939693i	1.89594	−	1.84537i	−0.866025	+	0.500000i	0.173648	−	0.984808i	−3.83066	+	1.39425i
241.9	0.342020	−	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	−1.64471	−	1.96009i	0.342020	+	0.939693i	−2.00395	−	1.72747i	−0.866025	+	0.500000i	0.173648	−	0.984808i	−2.40441	+	0.875134i
241.10	0.342020	−	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	−1.39177	−	1.65864i	0.342020	+	0.939693i	1.22000	+	2.34768i	−0.866025	+	0.500000i	0.173648	−	0.984808i	−2.03463	+	0.740544i
241.11	0.342020	−	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	−0.195288	−	0.232735i	0.342020	+	0.939693i	1.33464	+	2.28446i	−0.866025	+	0.500000i	0.173648	−	0.984808i	−0.285492	+	0.103911i
241.12	0.342020	−	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	0.367636	+	0.438132i	0.342020	+	0.939693i	−2.61193	+	0.421719i	−0.866025	+	0.500000i	0.173648	−	0.984808i	0.537448	−	0.195615i
241.13	0.342020	−	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	0.494314	+	0.589100i	0.342020	+	0.939693i	1.48242	−	2.19145i	−0.866025	+	0.500000i	0.173648	−	0.984808i	0.722638	−	0.263019i
241.14	0.342020	−	0.939693i	−0.766044	+	0.642788i	−0.766044	−	0.642788i	2.66876	+	3.18050i	0.342020	+	0.939693i	2.61323	+	0.413530i	−0.866025	+	0.500000i	0.173648	−	0.984808i	3.90147	−	1.42002i
409.1	−0.642788	−	0.766044i	−0.173648	−	0.984808i	−0.173648	+	0.984808i	−2.99934	+	0.528865i	−0.642788	+	0.766044i	2.53961	−	0.741884i	0.866025	−	0.500000i	−0.939693	+	0.342020i	2.33307	+	1.95768i
409.2	−0.642788	−	0.766044i	−0.173648	−	0.984808i	−0.173648	+	0.984808i	−1.67755	+	0.295797i	−0.642788	+	0.766044i	0.711004	−	2.54843i	0.866025	−	0.500000i	−0.939693	+	0.342020i	1.30490	+	1.09494i
409.3	−0.642788	−	0.766044i	−0.173648	−	0.984808i	−0.173648	+	0.984808i	−0.933464	+	0.164595i	−0.642788	+	0.766044i	−2.24821	−	1.39484i	0.866025	−	0.500000i	−0.939693	+	0.342020i	0.726106	+	0.609276i
409.4	−0.642788	−	0.766044i	−0.173648	−	0.984808i	−0.173648	+	0.984808i	0.400945	−	0.0706975i	−0.642788	+	0.766044i	−0.444783	+	2.60810i	0.866025	−	0.500000i	−0.939693	+	0.342020i	−0.311880	−	0.261698i
409.5	−0.642788	−	0.766044i	−0.173648	−	0.984808i	−0.173648	+	0.984808i	1.57868	−	0.278363i	−0.642788	+	0.766044i	1.21184	+	2.35190i	0.866025	−	0.500000i	−0.939693	+	0.342020i	−1.22799	−	1.03041i
409.6	−0.642788	−	0.766044i	−0.173648	−	0.984808i	−0.173648	+	0.984808i	3.04553	−	0.537009i	−0.642788	+	0.766044i	−2.64029	−	0.169924i	0.866025	−	0.500000i	−0.939693	+	0.342020i	−2.36900	−	1.98783i

See all 84 embeddings

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
133.bf	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	798.2.cj.b	yes	84
7.d	odd	6	1		798.2.ca.b	✓	84
19.f	odd	18	1		798.2.ca.b	✓	84
133.bf	even	18	1	inner	798.2.cj.b	yes	84

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
798.2.ca.b	✓	84	7.d	odd	6	1
798.2.ca.b	✓	84	19.f	odd	18	1
798.2.cj.b	yes	84	1.a	even	1	1	trivial
798.2.cj.b	yes	84	133.bf	even	18	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{5}^{84} + 15 T_{5}^{82} - 90 T_{5}^{81} + 213 T_{5}^{80} - 1680 T_{5}^{79} - 273 T_{5}^{78} + \cdots + 57\!\cdots\!96 $ T5^84 + 15*T5^82 - 90*T5^81 + 213*T5^80 - 1680*T5^79 - 273*T5^78 - 23454*T5^77 - 15258*T5^76 + 207270*T5^75 + 127338*T5^74 + 7728312*T5^73 + 10741496*T5^72 + 95937294*T5^71 - 537507*T5^70 - 819356358*T5^69 - 2409974379*T5^68 - 23770224924*T5^67 - 25212051844*T5^66 - 190023581262*T5^65 + 252903740559*T5^64 + 1733507358714*T5^63 + 7436656199439*T5^62 + 35471513511720*T5^61 + 60710749655737*T5^60 + 200789237643900*T5^59 - 254458280865759*T5^58 - 2220573500012526*T5^57 - 8994276637483020*T5^56 - 30837205975210272*T5^55 - 48576988105895494*T5^54 - 79057165145785014*T5^53 + 406248062757642642*T5^52 + 1801544211515820276*T5^51 + 6022963295560174638*T5^50 + 11242073594095815978*T5^49 + 12777588984977888853*T5^48 - 6795525437680760622*T5^47 - 121959243244520366100*T5^46 - 361175668924047969498*T5^45 - 557948333347755642336*T5^44 + 182870806375738242732*T5^43 + 1914380956500307399980*T5^42 + 1688663273186541493188*T5^41 - 1597656147869041424877*T5^40 + 2199871770672508519002*T5^39 + 34901218059222295559847*T5^38 + 54862362638063600112114*T5^37 - 44932470172378839916675*T5^36 - 236027689961466081904308*T5^35 - 215895454262425682752419*T5^34 + 224514027741227019168384*T5^33 + 323274203429378533039518*T5^32 - 396191764726127092307352*T5^31 - 451497195872051718910792*T5^30 + 1437186700579184848918662*T5^29 + 2647514689778837635696515*T5^28 - 966762314171617914185874*T5^27 - 1996064264846980733210535*T5^26 + 3548360063735361028335846*T5^25 + 738494911569234234903447*T5^24 - 8244015797933230581221532*T5^23 - 3856896139187588403281469*T5^22 + 7203369747583347436235070*T5^21 + 3535532306992349908577436*T5^20 - 5106928040090971310248716*T5^19 - 73212687472179264620052*T5^18 + 4509652051021118288640090*T5^17 + 615899531075383074263235*T5^16 - 598318941212023713752724*T5^15 + 271505573733989987042106*T5^14 + 266402877070640518612320*T5^13 + 235409029395662433007441*T5^12 - 61905598223634586418256*T5^11 - 64232922363608590612128*T5^10 + 37878131463559723070208*T5^9 + 4374057801302421590016*T5^8 - 6778115883558378624384*T5^7 - 825839206970574434688*T5^6 - 40841090298276756480*T5^5 + 213146495180987397120*T5^4 + 1284069336689590272*T5^3 + 19000664488869590016*T5^2 + 1108607360361357312*T5 + 575233757691088896 acting on $S_{2}^{\mathrm{new}}(798, [\chi])$.

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cj (of order \(18\), degree \(6\), minimal)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 241.14
Significant digits:
Format:

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