LMFDB - Newform orbit 930.2.br.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, 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:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $q$-expansion, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) = $ $ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $

$\operatorname{Tr}(f)(q) = $ $ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 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	$ a_{2} $			$ a_{3} $			$ a_{4} $			$ a_{5} $			$ a_{6} $			$ a_{7} $			$ a_{8} $			$ a_{9} $			$ a_{10} $
11.1	−0.951057	+	0.309017i	−1.68681	+	0.393302i	0.809017	−	0.587785i	0.866025	−	0.500000i	1.48271	−	0.895304i	0.503857	+	4.79388i	−0.587785	+	0.809017i	2.69063	−	1.32685i	−0.669131	+	0.743145i
11.2	−0.951057	+	0.309017i	−1.68179	+	0.414242i	0.809017	−	0.587785i	0.866025	−	0.500000i	1.47147	−	0.913668i	−0.309626	−	2.94590i	−0.587785	+	0.809017i	2.65681	−	1.39333i	−0.669131	+	0.743145i
11.3	−0.951057	+	0.309017i	−1.35745	−	1.07579i	0.809017	−	0.587785i	0.866025	−	0.500000i	1.62345	+	0.603659i	0.0557772	+	0.530685i	−0.587785	+	0.809017i	0.685360	+	2.92066i	−0.669131	+	0.743145i
11.4	−0.951057	+	0.309017i	−1.00587	+	1.41004i	0.809017	−	0.587785i	0.866025	−	0.500000i	0.520913	−	1.65186i	−0.0129897	−	0.123589i	−0.587785	+	0.809017i	−0.976447	−	2.83664i	−0.669131	+	0.743145i
11.5	−0.951057	+	0.309017i	−0.361945	−	1.69381i	0.809017	−	0.587785i	0.866025	−	0.500000i	0.867646	+	1.49906i	0.291242	+	2.77098i	−0.587785	+	0.809017i	−2.73799	+	1.22613i	−0.669131	+	0.743145i
11.6	−0.951057	+	0.309017i	0.164188	+	1.72425i	0.809017	−	0.587785i	0.866025	−	0.500000i	−0.688975	−	1.58912i	−0.487372	−	4.63703i	−0.587785	+	0.809017i	−2.94608	+	0.566203i	−0.669131	+	0.743145i
11.7	−0.951057	+	0.309017i	0.821805	+	1.52468i	0.809017	−	0.587785i	0.866025	−	0.500000i	−1.25273	−	1.19610i	0.122441	+	1.16495i	−0.587785	+	0.809017i	−1.64927	+	2.50597i	−0.669131	+	0.743145i
11.8	−0.951057	+	0.309017i	0.991446	−	1.42022i	0.809017	−	0.587785i	0.866025	−	0.500000i	−0.504048	+	1.65709i	−0.310184	−	2.95121i	−0.587785	+	0.809017i	−1.03407	−	2.81615i	−0.669131	+	0.743145i
11.9	−0.951057	+	0.309017i	1.11822	−	1.32272i	0.809017	−	0.587785i	0.866025	−	0.500000i	−0.654747	+	1.60353i	0.396236	+	3.76994i	−0.587785	+	0.809017i	−0.499172	−	2.95818i	−0.669131	+	0.743145i
11.10	−0.951057	+	0.309017i	1.48579	+	0.890187i	0.809017	−	0.587785i	0.866025	−	0.500000i	−1.68815	−	0.387484i	0.0245947	+	0.234003i	−0.587785	+	0.809017i	1.41514	+	2.64526i	−0.669131	+	0.743145i
11.11	−0.951057	+	0.309017i	1.51241	−	0.844159i	0.809017	−	0.587785i	0.866025	−	0.500000i	−1.17753	+	1.27020i	0.00579634	+	0.0551485i	−0.587785	+	0.809017i	1.57479	−	2.55344i	−0.669131	+	0.743145i
11.12	0.951057	−	0.309017i	−1.69764	−	0.343522i	0.809017	−	0.587785i	−0.866025	+	0.500000i	−1.72071	+	0.197892i	−0.487372	−	4.63703i	0.587785	−	0.809017i	2.76399	+	1.16636i	−0.669131	+	0.743145i
11.13	0.951057	−	0.309017i	−1.50746	+	0.852971i	0.809017	−	0.587785i	−0.866025	+	0.500000i	−1.17010	+	1.27705i	−0.0129897	−	0.123589i	0.587785	−	0.809017i	1.54488	−	2.57164i	−0.669131	+	0.743145i
11.14	0.951057	−	0.309017i	−1.43042	−	0.976675i	0.809017	−	0.587785i	−0.866025	+	0.500000i	−1.66222	−	0.486849i	0.122441	+	1.16495i	0.587785	−	0.809017i	1.09221	+	2.79411i	−0.669131	+	0.743145i
11.15	0.951057	−	0.309017i	−0.730003	−	1.57070i	0.809017	−	0.587785i	−0.866025	+	0.500000i	−1.17965	−	1.26824i	0.0245947	+	0.234003i	0.587785	−	0.809017i	−1.93419	+	2.29323i	−0.669131	+	0.743145i
11.16	0.951057	−	0.309017i	−0.587767	+	1.62927i	0.809017	−	0.587785i	−0.866025	+	0.500000i	−0.0555271	+	1.73116i	−0.309626	−	2.94590i	0.587785	−	0.809017i	−2.30906	−	1.91527i	−0.669131	+	0.743145i
11.17	0.951057	−	0.309017i	−0.567467	+	1.63645i	0.809017	−	0.587785i	−0.866025	+	0.500000i	−0.0340008	+	1.73172i	0.503857	+	4.79388i	0.587785	−	0.809017i	−2.35596	−	1.85727i	−0.669131	+	0.743145i
11.18	0.951057	−	0.309017i	0.928002	+	1.46247i	0.809017	−	0.587785i	−0.866025	+	0.500000i	1.33451	+	1.10412i	0.0557772	+	0.530685i	0.587785	−	0.809017i	−1.27762	+	2.71435i	−0.669131	+	0.743145i
11.19	0.951057	−	0.309017i	0.997625	−	1.41589i	0.809017	−	0.587785i	−0.866025	+	0.500000i	0.511264	−	1.65487i	0.00579634	+	0.0551485i	0.587785	−	0.809017i	−1.00949	−	2.82505i	−0.669131	+	0.743145i
11.20	0.951057	−	0.309017i	1.43236	−	0.973832i	0.809017	−	0.587785i	−0.866025	+	0.500000i	1.06132	−	1.36879i	0.396236	+	3.76994i	0.587785	−	0.809017i	1.10330	−	2.78975i	−0.669131	+	0.743145i

See next 80 embeddings (of 176 total)

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
31.h	odd	30	1	inner
93.p	even	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	930.2.br.a	✓	176
3.b	odd	2	1	inner	930.2.br.a	✓	176
31.h	odd	30	1	inner	930.2.br.a	✓	176
93.p	even	30	1	inner	930.2.br.a	✓	176

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
930.2.br.a	✓	176	1.a	even	1	1	trivial
930.2.br.a	✓	176	3.b	odd	2	1	inner
930.2.br.a	✓	176	31.h	odd	30	1	inner
930.2.br.a	✓	176	93.p	even	30	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{7}^{88} - 2 T_{7}^{87} - 42 T_{7}^{86} + 82 T_{7}^{85} + 457 T_{7}^{84} - 494 T_{7}^{83} + \cdots + 35\!\cdots\!16 $ T7^88 - 2*T7^87 - 42*T7^86 + 82*T7^85 + 457*T7^84 - 494*T7^83 + 13845*T7^82 - 11930*T7^81 - 630068*T7^80 + 215984*T7^79 + 12665689*T7^78 - 11573820*T7^77 - 61886226*T7^76 + 324844848*T7^75 - 3680630319*T7^74 - 171381916*T7^73 + 121046128578*T7^72 - 131941724906*T7^71 - 1740837898214*T7^70 + 3321257639172*T7^69 + 8330983903127*T7^68 - 45996150027474*T7^67 + 229011482233745*T7^66 + 401197746422616*T7^65 - 6041689934534111*T7^64 + 2800346618815690*T7^63 + 74808908116184505*T7^62 - 112137135911086278*T7^61 - 271889818234911559*T7^60 + 969367200278742598*T7^59 - 6377901180777713931*T7^58 + 4545540229178733552*T7^57 + 104503705912671853115*T7^56 - 184409806509230342894*T7^55 - 493747467957585594130*T7^54 + 1585693730095385588518*T7^53 - 2945386956925230627960*T7^52 + 486473096846792131028*T7^51 + 50411286926119946347298*T7^50 - 115849958137516487154358*T7^49 - 218320785869363939791079*T7^48 + 868114039951360067330758*T7^47 - 370355493551687676230994*T7^46 - 1021911868260102861279482*T7^45 + 7986445081617514995794366*T7^44 - 22608757241828586723342944*T7^43 - 42709292562970808076472835*T7^42 + 171570244870347371095258154*T7^41 + 197153971951320947527625643*T7^40 - 744712976838054126019445938*T7^39 - 803789516877511758090405688*T7^38 + 2614316888338990598938620598*T7^37 + 1367499093457991075089801956*T7^36 - 5483800469007702784039689730*T7^35 + 304183326404968964262141177*T7^34 + 1405936924381433458271176758*T7^33 + 11529148442101388235134353107*T7^32 - 26127488687127497951472354940*T7^31 + 35775418669903294872848049586*T7^30 - 41514860234586804456803343688*T7^29 + 47337886123897333926993925366*T7^28 - 76542335235182208467163078102*T7^27 + 117736524250341319132558831417*T7^26 - 115891211261287242357359749890*T7^25 + 86019532727741283998021490186*T7^24 - 95347130102051664201703730372*T7^23 + 123783300743014121481443465067*T7^22 - 105807173619001600105233545620*T7^21 + 59062413543700125848949490938*T7^20 - 36389461387090556945084071656*T7^19 + 33905783024809675645581879985*T7^18 - 25458909198762027719132697382*T7^17 + 11547701013335037323488230490*T7^16 - 2432311826885974140476062620*T7^15 - 382263408655585494950266517*T7^14 + 81739858872523213207153476*T7^13 + 553860582676731215651580808*T7^12 - 538116422007869170339358126*T7^11 + 253464319335500550649546807*T7^10 - 77120289105527619358849992*T7^9 + 17404081588240617879612381*T7^8 - 2909373563110684552104092*T7^7 + 329917154776436308153788*T7^6 - 30244123503054615697840*T7^5 + 2543401059654426211744*T7^4 + 8135729931649285824*T7^3 + 4892836606760647296*T7^2 + 252040175348180480*T7 + 3560424885135616 acting on $S_{2}^{\mathrm{new}}(930, [\chi])$.

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 11.22
Significant digits:
Format:

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