Properties

Label 935.2.f.b
Level $935$
Weight $2$
Character orbit 935.f
Analytic conductor $7.466$
Analytic rank $0$
Dimension $34$
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(441,935)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(935, base_ring=CyclotomicField(2))
 
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("935.441");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 935.f (of order \(2\), degree \(1\), 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: \(34\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 34 q - 6 q^{2} + 42 q^{4} - 18 q^{8} - 50 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 34 q - 6 q^{2} + 42 q^{4} - 18 q^{8} - 50 q^{9} + 8 q^{13} + 34 q^{16} + 52 q^{18} - 28 q^{19} + 16 q^{21} - 34 q^{25} + 28 q^{26} - 42 q^{32} + 22 q^{34} + 14 q^{35} - 150 q^{36} + 32 q^{38} - 12 q^{42} - 12 q^{43} + 26 q^{47} - 44 q^{49} + 6 q^{50} + 4 q^{51} + 62 q^{52} - 66 q^{53} - 34 q^{55} - 38 q^{59} + 24 q^{60} + 30 q^{64} - 22 q^{67} + 42 q^{68} + 64 q^{69} - 4 q^{70} + 178 q^{72} - 96 q^{76} + 14 q^{77} + 98 q^{81} - 40 q^{83} - 188 q^{84} + 10 q^{85} + 68 q^{86} + 50 q^{89} - 64 q^{93} + 52 q^{94} - 50 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
441.1 −2.71357 1.88783i 5.36347 1.00000i 5.12275i 1.94701i −9.12702 −0.563885 2.71357i
441.2 −2.71357 1.88783i 5.36347 1.00000i 5.12275i 1.94701i −9.12702 −0.563885 2.71357i
441.3 −2.66544 3.36068i 5.10456 1.00000i 8.95769i 3.62292i −8.27500 −8.29419 2.66544i
441.4 −2.66544 3.36068i 5.10456 1.00000i 8.95769i 3.62292i −8.27500 −8.29419 2.66544i
441.5 −2.21920 3.15959i 2.92486 1.00000i 7.01176i 3.92482i −2.05244 −6.98299 2.21920i
441.6 −2.21920 3.15959i 2.92486 1.00000i 7.01176i 3.92482i −2.05244 −6.98299 2.21920i
441.7 −2.06277 0.620881i 2.25501 1.00000i 1.28073i 0.540632i −0.526032 2.61451 2.06277i
441.8 −2.06277 0.620881i 2.25501 1.00000i 1.28073i 0.540632i −0.526032 2.61451 2.06277i
441.9 −1.83110 2.66006i 1.35293 1.00000i 4.87084i 2.65496i 1.18486 −4.07594 1.83110i
441.10 −1.83110 2.66006i 1.35293 1.00000i 4.87084i 2.65496i 1.18486 −4.07594 1.83110i
441.11 −1.70389 1.74029i 0.903257 1.00000i 2.96527i 0.100972i 1.86873 −0.0286124 1.70389i
441.12 −1.70389 1.74029i 0.903257 1.00000i 2.96527i 0.100972i 1.86873 −0.0286124 1.70389i
441.13 −1.02257 1.44697i −0.954349 1.00000i 1.47963i 1.42982i 3.02103 0.906284 1.02257i
441.14 −1.02257 1.44697i −0.954349 1.00000i 1.47963i 1.42982i 3.02103 0.906284 1.02257i
441.15 −0.478851 1.89263i −1.77070 1.00000i 0.906287i 1.08857i 1.80560 −0.582043 0.478851i
441.16 −0.478851 1.89263i −1.77070 1.00000i 0.906287i 1.08857i 1.80560 −0.582043 0.478851i
441.17 −0.368204 1.85231i −1.86443 1.00000i 0.682030i 2.84540i 1.42290 −0.431060 0.368204i
441.18 −0.368204 1.85231i −1.86443 1.00000i 0.682030i 2.84540i 1.42290 −0.431060 0.368204i
441.19 −0.0999015 0.941658i −1.99002 1.00000i 0.0940730i 4.23923i 0.398609 2.11328 0.0999015i
441.20 −0.0999015 0.941658i −1.99002 1.00000i 0.0940730i 4.23923i 0.398609 2.11328 0.0999015i
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 441.34
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 935.2.f.b 34
17.b even 2 1 inner 935.2.f.b 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
935.2.f.b 34 1.a even 1 1 trivial
935.2.f.b 34 17.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{17} + 3 T_{2}^{16} - 23 T_{2}^{15} - 71 T_{2}^{14} + 209 T_{2}^{13} + 673 T_{2}^{12} - 952 T_{2}^{11} - 3275 T_{2}^{10} + 2258 T_{2}^{9} + 8718 T_{2}^{8} - 2491 T_{2}^{7} - 12469 T_{2}^{6} + 427 T_{2}^{5} + 8660 T_{2}^{4} + \cdots - 56 \) acting on \(S_{2}^{\mathrm{new}}(935, [\chi])\). Copy content Toggle raw display