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Properties

Label 935.2.u.g
Level $935$
Weight $2$
Character orbit 935.u
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(86,935)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(935, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("935.86");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 935.u (of order \(5\), 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: \(68\)
Relative dimension: \(17\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 68 q + q^{2} - 23 q^{4} - 17 q^{5} - 13 q^{6} - 8 q^{7} + 18 q^{8} - 35 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 68 q + q^{2} - 23 q^{4} - 17 q^{5} - 13 q^{6} - 8 q^{7} + 18 q^{8} - 35 q^{9} - 4 q^{10} + 11 q^{11} + 44 q^{12} + 5 q^{13} - 17 q^{14} - 35 q^{16} + 17 q^{17} - 31 q^{18} + 15 q^{19} - 23 q^{20} - 12 q^{21} - 16 q^{22} + 48 q^{23} - 17 q^{24} - 17 q^{25} + 36 q^{26} + 12 q^{27} + 40 q^{28} + 16 q^{29} + 12 q^{30} + 8 q^{31} - 8 q^{32} - 24 q^{33} + 4 q^{34} + 12 q^{35} - 72 q^{36} + 4 q^{37} - 4 q^{38} + 10 q^{39} + 18 q^{40} + 6 q^{41} - 52 q^{42} - 76 q^{43} + 28 q^{44} + 120 q^{45} - 18 q^{46} - 46 q^{47} + 42 q^{48} - 31 q^{49} + q^{50} + 73 q^{52} + 57 q^{53} + 4 q^{54} - 19 q^{55} + 206 q^{56} - 18 q^{57} + 30 q^{58} - 13 q^{59} - 56 q^{60} - 12 q^{61} + 57 q^{62} + 19 q^{63} - 50 q^{64} - 10 q^{65} - 17 q^{66} + 104 q^{67} + 23 q^{68} - 52 q^{69} - 17 q^{70} - 61 q^{71} + 176 q^{72} + 4 q^{73} + 70 q^{74} - 10 q^{75} - 38 q^{76} + 23 q^{77} - 78 q^{78} - 16 q^{79} - 55 q^{80} + 49 q^{81} - 86 q^{82} + 10 q^{83} + 199 q^{84} + 17 q^{85} - 17 q^{86} - 120 q^{87} - 28 q^{88} + 90 q^{89} + 19 q^{90} - 22 q^{91} - 111 q^{92} - 21 q^{93} + 30 q^{94} + 15 q^{95} - 172 q^{96} - 18 q^{97} + 120 q^{98} + q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
86.1 −0.847374 + 2.60795i 1.85421 − 1.34716i −4.46532 − 3.24425i 0.309017 + 0.951057i 1.94212 + 5.97723i −2.22959 − 1.61989i 7.80773 − 5.67265i 0.696195 − 2.14267i −2.74216
86.2 −0.837174 + 2.57656i 0.184941 − 0.134368i −4.31975 − 3.13849i 0.309017 + 0.951057i 0.191378 + 0.589000i 1.79628 + 1.30507i 7.31938 − 5.31784i −0.910902 + 2.80347i −2.70915
86.3 −0.746937 + 2.29884i −1.85678 + 1.34903i −3.10870 − 2.25860i 0.309017 + 0.951057i −1.71430 − 5.27608i 3.37919 + 2.45512i 3.60315 − 2.61784i 0.700706 − 2.15655i −2.41714
86.4 −0.647786 + 1.99368i −2.43146 + 1.76656i −1.93710 − 1.40738i 0.309017 + 0.951057i −1.94689 − 5.99191i −1.25457 − 0.911496i 0.668848 − 0.485947i 1.86422 − 5.73748i −2.09628
86.5 −0.524657 + 1.61473i 1.96506 − 1.42770i −0.714046 − 0.518785i 0.309017 + 0.951057i 1.27437 + 3.92209i 2.46781 + 1.79297i −1.53481 + 1.11511i 0.896089 − 2.75788i −1.69782
86.6 −0.488525 + 1.50352i −0.566546 + 0.411620i −0.403896 − 0.293448i 0.309017 + 0.951057i −0.342109 − 1.05290i 0.316469 + 0.229928i −1.91943 + 1.39455i −0.775507 + 2.38677i −1.58090
86.7 −0.193798 + 0.596449i −1.56034 + 1.13366i 1.29984 + 0.944389i 0.309017 + 0.951057i −0.373776 − 1.15036i −4.11132 − 2.98705i −1.82993 + 1.32952i 0.222445 − 0.684614i −0.627143
86.8 −0.0950778 + 0.292619i 0.273990 − 0.199066i 1.54145 + 1.11993i 0.309017 + 0.951057i 0.0322001 + 0.0991017i 1.42795 + 1.03746i −0.972104 + 0.706275i −0.891607 + 2.74409i −0.307678
86.9 0.0701232 − 0.215817i 1.64421 − 1.19459i 1.57637 + 1.14530i 0.309017 + 0.951057i −0.142515 − 0.438617i 0.129519 + 0.0941011i 0.724886 − 0.526660i 0.349334 − 1.07514i 0.226923
86.10 0.173185 − 0.533008i −2.68178 + 1.94843i 1.36393 + 0.990953i 0.309017 + 0.951057i 0.574084 + 1.76685i −1.12131 − 0.814682i 1.67120 − 1.21420i 2.46853 − 7.59735i 0.560438
86.11 0.237733 − 0.731666i −0.571908 + 0.415516i 1.13922 + 0.827689i 0.309017 + 0.951057i 0.168057 + 0.517227i −2.97931 − 2.16460i 2.12120 − 1.54115i −0.772625 + 2.37790i 0.769319
86.12 0.348024 − 1.07111i 1.69818 − 1.23380i 0.591881 + 0.430027i 0.309017 + 0.951057i −0.730526 − 2.24833i −2.72711 − 1.98136i 2.48887 − 1.80827i 0.434502 − 1.33726i 1.12623
86.13 0.377550 − 1.16198i −2.39515 + 1.74018i 0.410380 + 0.298159i 0.309017 + 0.951057i 1.11776 + 3.44012i 3.81087 + 2.76876i 2.47827 − 1.80057i 1.78147 − 5.48281i 1.22178
86.14 0.509121 − 1.56691i 0.460061 − 0.334254i −0.577980 − 0.419927i 0.309017 + 0.951057i −0.289520 − 0.891051i 1.87944 + 1.36549i 1.71354 − 1.24496i −0.827121 + 2.54562i 1.64755
86.15 0.668333 − 2.05692i 2.22080 − 1.61350i −2.16621 − 1.57384i 0.309017 + 0.951057i −1.83461 − 5.64636i 1.95521 + 1.42054i −1.18558 + 0.861374i 1.40150 − 4.31337i 2.16277
86.16 0.842650 − 2.59341i 1.75431 − 1.27458i −4.39769 − 3.19511i 0.309017 + 0.951057i −1.82724 − 5.62366i −4.08625 − 2.96883i −7.57976 + 5.50702i 0.525988 − 1.61882i 2.72687
86.17 0.845592 − 2.60246i −2.22785 + 1.61863i −4.43976 − 3.22568i 0.309017 + 0.951057i 2.32857 + 7.16660i −0.653281 − 0.474636i −7.72136 + 5.60990i 1.41631 − 4.35895i 2.73639
256.1 −2.21158 + 1.60680i 0.248104 + 0.763585i 1.69122 − 5.20503i −0.809017 − 0.587785i −1.77563 − 1.29007i 1.27584 − 3.92663i 2.93371 + 9.02905i 1.90555 − 1.38446i 2.73366
256.2 −2.08625 + 1.51575i 0.502779 + 1.54740i 1.43692 − 4.42238i −0.809017 − 0.587785i −3.39439 − 2.46617i −1.38206 + 4.25356i 2.11170 + 6.49913i 0.285406 − 0.207360i 2.57875
256.3 −1.89362 + 1.37579i 0.897370 + 2.76182i 1.07494 − 3.30833i −0.809017 − 0.587785i −5.49897 − 3.99523i 0.709714 − 2.18427i 1.06946 + 3.29145i −4.39534 + 3.19340i 2.34064
See all 68 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 86.17
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 935.2.u.g ✓ 68
11.c even 5 1 inner 935.2.u.g ✓ 68
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
935.2.u.g ✓ 68 1.a even 1 1 trivial
935.2.u.g ✓ 68 11.c even 5 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{68} - T_{2}^{67} + 29 T_{2}^{66} - 36 T_{2}^{65} + 505 T_{2}^{64} - 664 T_{2}^{63} + \cdots + 71554681 \) acting on \(S_{2}^{\mathrm{new}}(935, [\chi])\). Copy content Toggle raw display