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Properties

Label 935.2.x.a
Level $935$
Weight $2$
Character orbit 935.x
Analytic conductor $7.466$
Analytic rank $0$
Dimension $104$
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(111,935)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(935, base_ring=CyclotomicField(8))
 
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("935.111");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 935.x (of order \(8\), degree \(4\), 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: \(104\)
Relative dimension: \(26\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 104 q + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 104 q + 8 q^{6} + 16 q^{14} - 56 q^{16} - 8 q^{17} - 16 q^{18} + 8 q^{19} + 32 q^{24} - 64 q^{26} - 48 q^{27} + 8 q^{29} + 32 q^{31} + 40 q^{32} - 32 q^{34} - 24 q^{35} - 32 q^{36} - 8 q^{37} + 16 q^{39} - 16 q^{40} + 8 q^{41} + 56 q^{42} - 8 q^{43} - 16 q^{44} - 16 q^{45} - 8 q^{46} + 112 q^{48} + 24 q^{50} + 48 q^{51} + 88 q^{52} - 32 q^{53} + 40 q^{54} - 64 q^{56} - 16 q^{58} - 8 q^{59} - 56 q^{60} - 32 q^{61} - 8 q^{62} + 152 q^{63} + 56 q^{67} + 8 q^{68} - 32 q^{69} - 16 q^{70} + 72 q^{71} + 64 q^{74} - 56 q^{76} - 8 q^{77} - 208 q^{78} + 16 q^{79} + 32 q^{80} + 152 q^{82} + 80 q^{83} + 80 q^{84} + 128 q^{86} - 216 q^{87} + 16 q^{88} + 48 q^{91} - 80 q^{92} - 32 q^{93} - 136 q^{94} + 8 q^{95} - 32 q^{96} + 32 q^{97} + 16 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
111.1 −1.94944 + 1.94944i 1.15179 + 0.477088i − 5.60060i 0.382683 − 0.923880i −3.17540 + 1.31529i 0.705062 + 1.70217i 7.01915 + 7.01915i −1.02231 − 1.02231i 1.05503 + 2.54706i
111.2 −1.90771 + 1.90771i 0.461560 + 0.191184i − 5.27870i −0.382683 + 0.923880i −1.24524 + 0.515797i −0.390452 − 0.942635i 6.25480 + 6.25480i −1.94483 − 1.94483i −1.03244 − 2.49254i
111.3 −1.88579 + 1.88579i −2.63645 − 1.09206i − 5.11244i −0.382683 + 0.923880i 7.03120 − 2.91242i 1.45697 + 3.51744i 5.86942 + 5.86942i 3.63699 + 3.63699i −1.02058 − 2.46391i
111.4 −1.53257 + 1.53257i −0.272386 − 0.112826i − 2.69754i −0.382683 + 0.923880i 0.590364 − 0.244537i −0.656132 − 1.58404i 1.06902 + 1.06902i −2.05986 − 2.05986i −0.829420 − 2.00240i
111.5 −1.42067 + 1.42067i 1.01001 + 0.418358i − 2.03662i 0.382683 − 0.923880i −2.02924 + 0.840538i −1.05409 − 2.54480i 0.0520238 + 0.0520238i −1.27623 − 1.27623i 0.768862 + 1.85620i
111.6 −1.34034 + 1.34034i 2.65950 + 1.10160i − 1.59303i −0.382683 + 0.923880i −5.04115 + 2.08811i 0.135641 + 0.327466i −0.545479 − 0.545479i 3.73808 + 3.73808i −0.725387 − 1.75124i
111.7 −1.30729 + 1.30729i 0.823047 + 0.340917i − 1.41801i 0.382683 − 0.923880i −1.52164 + 0.630283i 0.518406 + 1.25154i −0.760832 − 0.760832i −1.56014 − 1.56014i 0.707500 + 1.70806i
111.8 −0.911534 + 0.911534i 1.59205 + 0.659448i 0.338212i −0.382683 + 0.923880i −2.05232 + 0.850097i −1.56348 − 3.77458i −2.13136 − 2.13136i −0.0215717 − 0.0215717i −0.493319 − 1.19098i
111.9 −0.888602 + 0.888602i −1.61687 − 0.669730i 0.420771i 0.382683 − 0.923880i 2.03188 − 0.841632i 0.0826160 + 0.199453i −2.15110 − 2.15110i 0.0444133 + 0.0444133i 0.480908 + 1.16102i
111.10 −0.852223 + 0.852223i −1.86489 − 0.772464i 0.547433i 0.382683 − 0.923880i 2.24762 − 0.930993i −1.86941 − 4.51315i −2.17098 − 2.17098i 0.759805 + 0.759805i 0.461220 + 1.11348i
111.11 −0.498788 + 0.498788i −1.11477 − 0.461753i 1.50242i −0.382683 + 0.923880i 0.786351 − 0.325717i 0.793340 + 1.91529i −1.74697 − 1.74697i −1.09182 − 1.09182i −0.269942 − 0.651698i
111.12 −0.380134 + 0.380134i −0.105432 − 0.0436713i 1.71100i 0.382683 − 0.923880i 0.0566792 − 0.0234773i 1.65208 + 3.98848i −1.41068 − 1.41068i −2.11211 − 2.11211i 0.205727 + 0.496669i
111.13 −0.188630 + 0.188630i −1.45008 − 0.600643i 1.92884i −0.382683 + 0.923880i 0.386828 − 0.160229i 0.0964042 + 0.232740i −0.741098 − 0.741098i −0.379362 − 0.379362i −0.102086 − 0.246457i
111.14 −0.0823761 + 0.0823761i 0.0979897 + 0.0405887i 1.98643i 0.382683 − 0.923880i −0.0114155 + 0.00472847i −0.0207701 − 0.0501436i −0.328386 − 0.328386i −2.11337 − 2.11337i 0.0445816 + 0.107630i
111.15 −0.0523789 + 0.0523789i 2.13029 + 0.882393i 1.99451i −0.382683 + 0.923880i −0.157801 + 0.0653633i 1.56686 + 3.78273i −0.209228 − 0.209228i 1.63818 + 1.63818i −0.0283473 − 0.0684363i
111.16 0.101353 − 0.101353i −2.55559 − 1.05856i 1.97946i −0.382683 + 0.923880i −0.366304 + 0.151728i −1.55091 − 3.74423i 0.403329 + 0.403329i 3.28917 + 3.28917i 0.0548517 + 0.132424i
111.17 0.276508 − 0.276508i −2.87590 − 1.19124i 1.84709i 0.382683 − 0.923880i −1.12460 + 0.465823i −0.836970 − 2.02062i 1.06375 + 1.06375i 4.73043 + 4.73043i −0.149645 − 0.361275i
111.18 0.564735 − 0.564735i 2.35305 + 0.974666i 1.36215i 0.382683 − 0.923880i 1.87928 − 0.778423i 0.973162 + 2.34942i 1.89872 + 1.89872i 2.46556 + 2.46556i −0.305633 − 0.737862i
111.19 0.760263 − 0.760263i −0.0562862 − 0.0233145i 0.843999i −0.382683 + 0.923880i −0.0605175 + 0.0250672i 0.425036 + 1.02613i 2.16219 + 2.16219i −2.11870 − 2.11870i 0.411452 + 0.993332i
111.20 0.770953 − 0.770953i −1.83435 − 0.759813i 0.811262i 0.382683 − 0.923880i −1.99998 + 0.828419i 0.803583 + 1.94002i 2.16735 + 2.16735i 0.666210 + 0.666210i −0.417237 − 1.00730i
See next 80 embeddings (of 104 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 111.26
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.d even 8 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 935.2.x.a ✓ 104
17.d even 8 1 inner 935.2.x.a ✓ 104
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
935.2.x.a ✓ 104 1.a even 1 1 trivial
935.2.x.a ✓ 104 17.d even 8 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{104} + 354 T_{2}^{100} - 8 T_{2}^{99} + 96 T_{2}^{97} + 56719 T_{2}^{96} - 1984 T_{2}^{95} + \cdots + 18496 \) acting on \(S_{2}^{\mathrm{new}}(935, [\chi])\). Copy content Toggle raw display