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Properties

Label 935.2.i.b
Level $935$
Weight $2$
Character orbit 935.i
Analytic conductor $7.466$
Analytic rank $0$
Dimension $68$
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: \(68\)
Relative dimension: \(34\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 68 q - 76 q^{4} - 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 68 q - 76 q^{4} - 4 q^{6} + 4 q^{10} + 20 q^{12} - 16 q^{13} + 20 q^{14} + 100 q^{16} - 8 q^{17} + 64 q^{18} - 32 q^{21} - 4 q^{22} + 4 q^{23} - 16 q^{24} + 24 q^{27} + 20 q^{28} + 28 q^{31} - 72 q^{34} + 20 q^{35} - 28 q^{37} - 24 q^{38} - 8 q^{39} + 8 q^{40} + 4 q^{41} - 8 q^{45} - 16 q^{46} + 4 q^{47} + 56 q^{48} + 12 q^{50} - 88 q^{51} + 124 q^{52} - 124 q^{54} + 68 q^{55} - 136 q^{56} + 28 q^{57} + 4 q^{58} + 16 q^{61} - 28 q^{62} + 36 q^{63} - 188 q^{64} + 52 q^{67} - 40 q^{68} + 160 q^{69} - 20 q^{71} - 164 q^{72} - 56 q^{73} - 64 q^{74} + 200 q^{78} - 180 q^{81} + 108 q^{82} + 152 q^{84} - 4 q^{85} + 296 q^{86} - 8 q^{88} - 180 q^{89} - 96 q^{91} - 48 q^{92} + 12 q^{95} + 104 q^{96} + 24 q^{97} - 180 q^{98} + 8 q^{99}+O(q^{100}) \) 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 − 2.78053i 1.49358 + 1.49358i −5.73134 −0.707107 − 0.707107i 4.15294 − 4.15294i −1.99585 + 1.99585i 10.3751i 1.46156i −1.96613 + 1.96613i
166.2 − 2.71929i −0.297237 − 0.297237i −5.39451 −0.707107 − 0.707107i −0.808273 + 0.808273i 2.60582 − 2.60582i 9.23065i − 2.82330i −1.92283 + 1.92283i
166.3 − 2.67176i −2.32415 − 2.32415i −5.13832 0.707107 + 0.707107i −6.20959 + 6.20959i 0.0203913 − 0.0203913i 8.38485i 7.80338i 1.88922 − 1.88922i
166.4 − 2.66431i 0.661609 + 0.661609i −5.09852 0.707107 + 0.707107i 1.76273 − 1.76273i 1.03241 − 1.03241i 8.25541i − 2.12455i 1.88395 − 1.88395i
166.5 − 2.48918i 1.94346 + 1.94346i −4.19601 0.707107 + 0.707107i 4.83762 − 4.83762i −3.01878 + 3.01878i 5.46627i 4.55407i 1.76012 − 1.76012i
166.6 − 2.21255i −1.83443 − 1.83443i −2.89538 −0.707107 − 0.707107i −4.05876 + 4.05876i −3.31719 + 3.31719i 1.98106i 3.73025i −1.56451 + 1.56451i
166.7 − 2.00659i 0.318160 + 0.318160i −2.02642 −0.707107 − 0.707107i 0.638418 − 0.638418i −2.28557 + 2.28557i 0.0530053i − 2.79755i −1.41888 + 1.41888i
166.8 − 1.82950i −1.37469 − 1.37469i −1.34707 0.707107 + 0.707107i −2.51499 + 2.51499i −0.925942 + 0.925942i − 1.19454i 0.779535i 1.29365 − 1.29365i
166.9 − 1.70941i −0.0266656 − 0.0266656i −0.922092 0.707107 + 0.707107i −0.0455826 + 0.0455826i −3.22992 + 3.22992i − 1.84259i − 2.99858i 1.20874 − 1.20874i
166.10 − 1.68444i −2.34628 − 2.34628i −0.837330 −0.707107 − 0.707107i −3.95216 + 3.95216i 2.36804 − 2.36804i − 1.95845i 8.01007i −1.19108 + 1.19108i
166.11 − 1.61922i 0.541701 + 0.541701i −0.621860 0.707107 + 0.707107i 0.877131 − 0.877131i 3.24324 − 3.24324i − 2.23151i − 2.41312i 1.14496 − 1.14496i
166.12 − 1.11862i 1.96846 + 1.96846i 0.748680 −0.707107 − 0.707107i 2.20197 − 2.20197i 2.59112 − 2.59112i − 3.07474i 4.74967i −0.790987 + 0.790987i
166.13 − 1.09860i −2.22104 − 2.22104i 0.793083 0.707107 + 0.707107i −2.44003 + 2.44003i 2.55358 − 2.55358i − 3.06847i 6.86603i 0.776826 − 0.776826i
166.14 − 0.972034i −0.478406 − 0.478406i 1.05515 −0.707107 − 0.707107i −0.465027 + 0.465027i 0.950800 − 0.950800i − 2.96971i − 2.54226i −0.687332 + 0.687332i
166.15 − 0.692238i 1.23006 + 1.23006i 1.52081 0.707107 + 0.707107i 0.851493 − 0.851493i −0.827991 + 0.827991i − 2.43724i 0.0260828i 0.489486 − 0.489486i
166.16 − 0.570806i 2.39792 + 2.39792i 1.67418 0.707107 + 0.707107i 1.36875 − 1.36875i 2.12451 − 2.12451i − 2.09725i 8.50005i 0.403621 − 0.403621i
166.17 − 0.513342i 2.03291 + 2.03291i 1.73648 −0.707107 − 0.707107i 1.04358 − 1.04358i −3.46215 + 3.46215i − 1.91809i 5.26546i −0.362988 + 0.362988i
166.18 − 0.162038i −0.303160 − 0.303160i 1.97374 0.707107 + 0.707107i −0.0491235 + 0.0491235i 0.576859 − 0.576859i − 0.643898i − 2.81619i 0.114578 − 0.114578i
166.19 0.00994945i 0.565662 + 0.565662i 1.99990 −0.707107 − 0.707107i −0.00562803 + 0.00562803i 1.45741 − 1.45741i 0.0397968i − 2.36005i 0.00703533 − 0.00703533i
166.20 0.288468i −1.68319 − 1.68319i 1.91679 −0.707107 − 0.707107i 0.485548 − 0.485548i 1.35603 − 1.35603i 1.12987i 2.66628i 0.203978 − 0.203978i
See all 68 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 166.34
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.b ✓ 68
17.c even 4 1 inner 935.2.i.b ✓ 68
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
935.2.i.b ✓ 68 1.a even 1 1 trivial
935.2.i.b ✓ 68 17.c even 4 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{68} + 106 T_{2}^{66} + 5343 T_{2}^{64} + 170460 T_{2}^{62} + 3865165 T_{2}^{60} + 66312466 T_{2}^{58} + \cdots + 18496 \) acting on \(S_{2}^{\mathrm{new}}(935, [\chi])\). Copy content Toggle raw display