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Properties

Label 547.2.m.a
Level $547$
Weight $2$
Character orbit 547.m
Analytic conductor $4.368$
Analytic rank $0$
Dimension $3168$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [547,2,Mod(10,547)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(547, base_ring=CyclotomicField(182))
 
chi = DirichletCharacter(H, H._module([60]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("547.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.m (of order \(91\), degree \(72\), 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: \(4.36781699056\)
Analytic rank: \(0\)
Dimension: \(3168\)
Relative dimension: \(44\) over \(\Q(\zeta_{91})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{91}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
10.1 −1.43254 − 2.41657i −0.00191599 − 0.00839448i −2.82779 + 5.16906i 2.23230 + 0.0770965i −0.0175412 + 0.0166555i −4.60768 + 0.640360i 10.9271 − 0.377388i 2.70284 − 1.30162i −3.01155 − 5.50497i
10.2 −1.38950 − 2.34398i −0.559135 − 2.44973i −2.60363 + 4.75932i −2.63335 − 0.0909474i −4.96519 + 4.71450i 0.746366 − 0.103727i 9.32698 − 0.322123i −2.98564 + 1.43781i 3.44587 + 6.29889i
10.3 −1.36435 − 2.30154i 0.713317 + 3.12524i −2.47578 + 4.52561i −3.57878 − 0.123599i 6.21968 − 5.90565i −0.332062 + 0.0461487i 8.44582 − 0.291691i −6.55543 + 3.15693i 4.59823 + 8.40534i
10.4 −1.21694 − 2.05288i 0.474632 + 2.07950i −1.77350 + 3.24187i 2.57302 + 0.0888638i 3.69137 − 3.50500i 2.57249 − 0.357516i 4.04333 − 0.139643i −1.39614 + 0.672344i −2.94880 − 5.39026i
10.5 −1.19472 − 2.01540i −0.168315 − 0.737438i −1.67460 + 3.06109i −1.16754 − 0.0403228i −1.28514 + 1.22026i 4.11811 − 0.572320i 3.48700 − 0.120429i 2.18742 − 1.05341i 1.31362 + 2.40123i
10.6 −1.11993 − 1.88923i 0.187104 + 0.819754i −1.35508 + 2.47702i −1.48051 − 0.0511319i 1.33916 − 1.27155i −2.38045 + 0.330826i 1.80741 − 0.0624220i 2.06592 − 0.994893i 1.56147 + 2.85429i
10.7 −1.11775 − 1.88556i −0.271817 − 1.19091i −1.34608 + 2.46058i 3.31408 + 0.114457i −1.94170 + 1.84367i 0.214643 − 0.0298303i 1.76284 − 0.0608827i 1.35853 − 0.654232i −3.48851 − 6.37683i
10.8 −1.10037 − 1.85624i −0.473626 − 2.07509i −1.27492 + 2.33049i 1.13411 + 0.0391684i −3.33070 + 3.16254i 0.250897 − 0.0348688i 1.41565 − 0.0488921i −1.37878 + 0.663987i −1.17524 − 2.14827i
10.9 −0.929069 − 1.56726i −0.617025 − 2.70336i −0.633268 + 1.15758i −0.691646 − 0.0238872i −3.66362 + 3.47865i −4.21969 + 0.586437i −1.23913 + 0.0427955i −4.22454 + 2.03443i 0.605149 + 1.10618i
10.10 −0.900824 − 1.51962i 0.668884 + 2.93057i −0.537874 + 0.983208i 1.50378 + 0.0519357i 3.85080 − 3.65638i −3.52663 + 0.490119i −1.55238 + 0.0536140i −5.43795 + 2.61878i −1.27572 − 2.33196i
10.11 −0.882718 − 1.48907i 0.304921 + 1.33595i −0.478271 + 0.874256i −3.64866 − 0.126013i 1.72016 − 1.63331i 2.07032 − 0.287726i −1.73602 + 0.0599566i 1.01113 − 0.486934i 3.03310 + 5.54435i
10.12 −0.807206 − 1.36169i 0.219615 + 0.962195i −0.242743 + 0.443723i −0.516600 − 0.0178417i 1.13294 − 1.07574i −2.71722 + 0.377630i −2.36389 + 0.0816410i 1.82532 − 0.879027i 0.392708 + 0.717851i
10.13 −0.671741 − 1.13317i −0.619707 − 2.71511i 0.127033 − 0.232210i −2.49729 − 0.0862482i −2.66041 + 2.52609i 1.97865 − 0.274985i −2.98152 + 0.102972i −4.28489 + 2.06350i 1.57980 + 2.88779i
10.14 −0.607931 − 1.02553i 0.696260 + 3.05052i 0.277745 − 0.507704i −0.411634 − 0.0142165i 2.70512 − 2.56854i 3.12156 − 0.433823i −3.07245 + 0.106112i −6.11797 + 2.94626i 0.235665 + 0.430785i
10.15 −0.575837 − 0.971390i −0.152308 − 0.667306i 0.347865 − 0.635880i 0.600736 + 0.0207475i −0.560510 + 0.532210i 0.619289 − 0.0860666i −3.07514 + 0.106205i 2.28081 − 1.09838i −0.325773 − 0.595497i
10.16 −0.572243 − 0.965327i −0.717695 − 3.14443i 0.355481 − 0.649802i 3.54444 + 0.122413i −2.62470 + 2.49219i 4.44174 − 0.617298i −3.07374 + 0.106157i −6.66943 + 3.21183i −1.91011 − 3.49159i
10.17 −0.449712 − 0.758628i −0.258554 − 1.13280i 0.586600 − 1.07228i 0.442256 + 0.0152741i −0.743097 + 0.705579i −1.14748 + 0.159473i −2.84002 + 0.0980850i 1.48653 − 0.715873i −0.187301 − 0.342377i
10.18 −0.432175 − 0.729044i 0.215157 + 0.942665i 0.615146 − 1.12446i 3.24535 + 0.112084i 0.594259 − 0.564255i 2.06386 − 0.286828i −2.77965 + 0.0959999i 1.86058 − 0.896009i −1.32084 − 2.41444i
10.19 −0.348818 − 0.588427i 0.465635 + 2.04008i 0.735303 − 1.34410i 2.83356 + 0.0978618i 1.03802 − 0.985608i −4.08637 + 0.567909i −2.41467 + 0.0833947i −1.24220 + 0.598212i −0.930811 − 1.70148i
10.20 −0.290706 − 0.490397i 0.429128 + 1.88013i 0.803896 − 1.46948i −2.18526 − 0.0754717i 0.797261 − 0.757008i −1.33797 + 0.185946i −2.09382 + 0.0723137i −0.647842 + 0.311984i 0.598256 + 1.09358i
See next 80 embeddings (of 3168 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 10.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
547.m even 91 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 547.2.m.a ✓ 3168
547.m even 91 1 inner 547.2.m.a ✓ 3168
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
547.2.m.a ✓ 3168 1.a even 1 1 trivial
547.2.m.a ✓ 3168 547.m even 91 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(547, [\chi])\).