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Properties

Label 935.2.i.a
Level $935$
Weight $2$
Character orbit 935.i
Analytic conductor $7.466$
Analytic rank $0$
Dimension $52$
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] = [935,2,Mod(166,935)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(935, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("935.166");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 935.i (of order \(4\), degree \(2\), 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: \(7.46601258899\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 52 q - 44 q^{4} - 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 52 q - 44 q^{4} - 4 q^{6} + 4 q^{10} + 20 q^{12} + 16 q^{13} + 12 q^{14} + 36 q^{16} - 64 q^{18} + 8 q^{20} + 32 q^{21} + 4 q^{22} + 4 q^{23} - 16 q^{24} - 24 q^{27} + 20 q^{28} - 4 q^{31} - 16 q^{33} + 64 q^{34} - 20 q^{35} + 4 q^{37} + 72 q^{38} + 40 q^{39} + 8 q^{40} + 4 q^{41} - 8 q^{44} - 8 q^{45} - 16 q^{46} + 84 q^{47} - 136 q^{48} - 12 q^{50} - 24 q^{51} - 124 q^{52} + 52 q^{54} - 52 q^{55} - 16 q^{56} + 52 q^{57} + 4 q^{58} - 48 q^{61} - 28 q^{62} - 36 q^{63} - 60 q^{64} - 28 q^{67} + 72 q^{68} - 64 q^{69} - 52 q^{71} + 164 q^{72} + 64 q^{73} - 32 q^{74} - 40 q^{78} - 16 q^{80} + 92 q^{81} - 84 q^{82} - 8 q^{84} + 12 q^{85} - 136 q^{86} + 8 q^{88} + 108 q^{89} + 32 q^{90} + 64 q^{91} - 48 q^{92} + 4 q^{95} + 104 q^{96} - 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
166.1 − 2.60760i −1.35198 − 1.35198i −4.79959 −0.707107 − 0.707107i −3.52543 + 3.52543i −1.55329 + 1.55329i 7.30023i 0.655712i −1.84385 + 1.84385i
166.2 − 2.35531i −0.355054 − 0.355054i −3.54749 0.707107 + 0.707107i −0.836263 + 0.836263i −2.36379 + 2.36379i 3.64482i − 2.74787i 1.66546 − 1.66546i
166.3 − 1.99415i −1.07054 − 1.07054i −1.97664 −0.707107 − 0.707107i −2.13482 + 2.13482i 1.99059 − 1.99059i − 0.0465866i − 0.707878i −1.41008 + 1.41008i
166.4 − 1.77851i 0.931662 + 0.931662i −1.16311 −0.707107 − 0.707107i 1.65697 − 1.65697i −0.607510 + 0.607510i − 1.48841i − 1.26401i −1.25760 + 1.25760i
166.5 − 1.75302i 0.978795 + 0.978795i −1.07307 0.707107 + 0.707107i 1.71585 − 1.71585i 2.16678 − 2.16678i − 1.62492i − 1.08392i 1.23957 − 1.23957i
166.6 − 1.72772i 2.09523 + 2.09523i −0.985009 0.707107 + 0.707107i 3.61997 − 3.61997i −0.430808 + 0.430808i − 1.75362i 5.78001i 1.22168 − 1.22168i
166.7 − 1.31512i −1.39550 − 1.39550i 0.270472 0.707107 + 0.707107i −1.83525 + 1.83525i 0.0733086 − 0.0733086i − 2.98593i 0.894856i 0.929927 − 0.929927i
166.8 − 0.668828i −0.454545 − 0.454545i 1.55267 0.707107 + 0.707107i −0.304012 + 0.304012i 2.44978 − 2.44978i − 2.37612i − 2.58678i 0.472933 − 0.472933i
166.9 − 0.623779i 1.21809 + 1.21809i 1.61090 −0.707107 − 0.707107i 0.759820 − 0.759820i 0.546797 − 0.546797i − 2.25240i − 0.0325074i −0.441079 + 0.441079i
166.10 − 0.558632i −0.429846 − 0.429846i 1.68793 −0.707107 − 0.707107i −0.240126 + 0.240126i −3.14781 + 3.14781i − 2.06020i − 2.63046i −0.395013 + 0.395013i
166.11 − 0.435619i −1.84894 − 1.84894i 1.81024 0.707107 + 0.707107i −0.805433 + 0.805433i −2.56176 + 2.56176i − 1.65981i 3.83715i 0.308029 − 0.308029i
166.12 − 0.306400i −0.878850 − 0.878850i 1.90612 −0.707107 − 0.707107i −0.269280 + 0.269280i 3.13909 − 3.13909i − 1.19684i − 1.45524i −0.216658 + 0.216658i
166.13 − 0.222708i 0.949203 + 0.949203i 1.95040 0.707107 + 0.707107i 0.211395 − 0.211395i 0.107185 − 0.107185i − 0.879788i − 1.19803i 0.157479 − 0.157479i
166.14 0.486397i 1.92200 + 1.92200i 1.76342 0.707107 + 0.707107i −0.934856 + 0.934856i −1.74752 + 1.74752i 1.83051i 4.38818i −0.343934 + 0.343934i
166.15 0.489852i −0.256489 − 0.256489i 1.76004 −0.707107 − 0.707107i 0.125642 − 0.125642i −2.47716 + 2.47716i 1.84187i − 2.86843i 0.346378 − 0.346378i
166.16 1.19361i 0.966531 + 0.966531i 0.575292 −0.707107 − 0.707107i −1.15366 + 1.15366i 3.57908 − 3.57908i 3.07390i − 1.13163i 0.844011 − 0.844011i
166.17 1.22734i −0.309336 − 0.309336i 0.493630 0.707107 + 0.707107i 0.379661 − 0.379661i 1.43026 − 1.43026i 3.06054i − 2.80862i −0.867862 + 0.867862i
166.18 1.46312i −0.699653 − 0.699653i −0.140729 0.707107 + 0.707107i 1.02368 − 1.02368i −1.81561 + 1.81561i 2.72034i − 2.02097i −1.03458 + 1.03458i
166.19 1.51713i −1.91091 − 1.91091i −0.301679 −0.707107 − 0.707107i 2.89910 − 2.89910i −0.183243 + 0.183243i 2.57657i 4.30316i 1.07277 − 1.07277i
166.20 1.77001i 1.68501 + 1.68501i −1.13294 0.707107 + 0.707107i −2.98248 + 2.98248i 2.82405 − 2.82405i 1.53471i 2.67851i −1.25159 + 1.25159i
See all 52 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 166.26
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.c even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 935.2.i.a ✓ 52
17.c even 4 1 inner 935.2.i.a ✓ 52
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
935.2.i.a ✓ 52 1.a even 1 1 trivial
935.2.i.a ✓ 52 17.c even 4 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{52} + 74 T_{2}^{50} + 2559 T_{2}^{48} + 54972 T_{2}^{46} + 822555 T_{2}^{44} + 9111646 T_{2}^{42} + \cdots + 18496 \) acting on \(S_{2}^{\mathrm{new}}(935, [\chi])\). Copy content Toggle raw display