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Properties

Label 935.2.u.e
Level $935$
Weight $2$
Character orbit 935.u
Analytic conductor $7.466$
Analytic rank $0$
Dimension $60$
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: \(60\)
Relative dimension: \(15\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 60 q - q^{2} + 10 q^{3} - 19 q^{4} + 15 q^{5} + 18 q^{6} + 14 q^{7} + 8 q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 60 q - q^{2} + 10 q^{3} - 19 q^{4} + 15 q^{5} + 18 q^{6} + 14 q^{7} + 8 q^{8} - 9 q^{9} - 14 q^{10} + 15 q^{11} - 84 q^{12} + q^{13} - q^{14} - 10 q^{15} - 29 q^{16} + 15 q^{17} - 13 q^{18} - 8 q^{19} + 24 q^{20} + 28 q^{22} - 78 q^{23} + 15 q^{24} - 15 q^{25} + 20 q^{26} + 22 q^{27} - 47 q^{28} - 11 q^{29} + 12 q^{30} + 10 q^{32} - 12 q^{33} - 14 q^{34} + 11 q^{35} + 27 q^{36} + 26 q^{37} + 87 q^{38} - 14 q^{39} - 8 q^{40} - 14 q^{41} - 27 q^{42} + 28 q^{43} - 56 q^{45} + 39 q^{46} + 45 q^{47} + 16 q^{48} - 17 q^{49} - q^{50} - 10 q^{51} + 24 q^{52} + 65 q^{53} - 94 q^{54} + 5 q^{55} - 144 q^{56} + 32 q^{57} + 48 q^{58} + 29 q^{59} - 21 q^{60} - 70 q^{61} - 73 q^{62} + 12 q^{63} - 32 q^{64} - 6 q^{65} + 130 q^{66} - 124 q^{67} + 24 q^{68} + 17 q^{69} + q^{70} + 4 q^{71} - 154 q^{72} - 49 q^{73} + 60 q^{74} + 52 q^{76} - 37 q^{77} - 62 q^{78} - 28 q^{79} + 24 q^{80} - 9 q^{81} + 122 q^{82} - 48 q^{83} - 88 q^{84} - 15 q^{85} - 62 q^{86} - 14 q^{87} + 114 q^{88} - 116 q^{89} + 18 q^{90} + 21 q^{91} + 83 q^{92} + 101 q^{93} - 75 q^{94} + 8 q^{95} - 53 q^{96} + 36 q^{97} + 20 q^{98} - 85 q^{99}+O(q^{100}) \) 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 −0.787755 + 2.42446i 2.54383 − 1.84820i −3.63942 − 2.64419i −0.309017 − 0.951057i 2.47697 + 7.62334i 3.36890 + 2.44765i 5.15297 − 3.74385i 2.12817 − 6.54982i 2.54923
86.2 −0.766629 + 2.35944i −0.0390857 + 0.0283975i −3.36120 − 2.44206i −0.309017 − 0.951057i −0.0370378 − 0.113991i −0.163849 − 0.119043i 4.32457 − 3.14198i −0.926330 + 2.85095i 2.48086
86.3 −0.758639 + 2.33485i −0.475734 + 0.345641i −3.25796 − 2.36704i −0.309017 − 0.951057i −0.446110 − 1.37299i −2.53062 − 1.83860i 4.02602 − 2.92507i −0.820196 + 2.52430i 2.45501
86.4 −0.451678 + 1.39012i 1.47825 − 1.07401i −0.110388 − 0.0802017i −0.309017 − 0.951057i 0.825315 + 2.54006i −1.14080 − 0.828841i −2.20366 + 1.60106i 0.104676 − 0.322159i 1.46166
86.5 −0.222212 + 0.683899i 0.430848 − 0.313029i 1.19969 + 0.871629i −0.309017 − 0.951057i 0.118341 + 0.364215i 3.99404 + 2.90184i −2.02621 + 1.47213i −0.839409 + 2.58343i 0.719094
86.6 −0.0464910 + 0.143084i −1.82073 + 1.32284i 1.59972 + 1.16227i −0.309017 − 0.951057i −0.104630 − 0.322018i 1.04542 + 0.759544i −0.484105 + 0.351723i 0.638101 − 1.96387i 0.150448
86.7 0.00401722 − 0.0123637i 2.24406 − 1.63040i 1.61790 + 1.17547i −0.309017 − 0.951057i −0.0111430 − 0.0342946i −1.38422 − 1.00569i 0.0420671 − 0.0305635i 1.45052 − 4.46426i −0.0130000
86.8 0.276504 − 0.850993i 1.40482 − 1.02066i 0.970300 + 0.704964i −0.309017 − 0.951057i −0.480138 − 1.47771i 1.29595 + 0.941562i 2.31601 − 1.68268i 0.00472467 − 0.0145410i −0.894787
86.9 0.371437 − 1.14317i −2.02600 + 1.47198i 0.449172 + 0.326342i −0.309017 − 0.951057i 0.930181 + 2.86280i 1.64025 + 1.19171i 2.48477 − 1.80529i 1.01092 − 3.11129i −1.20200
86.10 0.384223 − 1.18252i −0.884860 + 0.642888i 0.367317 + 0.266872i −0.309017 − 0.951057i 0.420242 + 1.29337i −2.64934 − 1.92485i 2.46853 − 1.79349i −0.557379 + 1.71544i −1.24337
86.11 0.566396 − 1.74319i 2.50231 − 1.81804i −1.09987 − 0.799100i −0.309017 − 0.951057i −1.75188 − 5.39173i −2.95953 − 2.15022i 0.949748 − 0.690032i 2.02926 − 6.24543i −1.83290
86.12 0.577697 − 1.77797i −2.19127 + 1.59205i −1.20940 − 0.878682i −0.309017 − 0.951057i 1.56473 + 4.81574i 0.0901138 + 0.0654715i 0.763923 − 0.555023i 1.33999 − 4.12408i −1.86947
86.13 0.640173 − 1.97025i 1.48378 − 1.07803i −1.85403 − 1.34703i −0.309017 − 0.951057i −1.17411 − 3.61355i 4.11242 + 2.98785i −0.488898 + 0.355206i 0.112411 − 0.345966i −2.07164
86.14 0.804943 − 2.47736i 1.55278 − 1.12816i −3.87135 − 2.81270i −0.309017 − 0.951057i −1.54496 − 4.75490i −0.454050 − 0.329886i −5.86955 + 4.26448i 0.211329 − 0.650404i −2.60485
86.15 0.835063 − 2.57006i −0.348902 + 0.253492i −4.28985 − 3.11676i −0.309017 − 0.951057i 0.360135 + 1.10838i 1.47139 + 1.06902i −7.22010 + 5.24571i −0.869577 + 2.67628i −2.70232
256.1 −2.22358 + 1.61552i −1.00724 − 3.09998i 1.71634 − 5.28236i 0.809017 + 0.587785i 7.24777 + 5.26581i −1.11929 + 3.44483i 3.01869 + 9.29057i −6.16827 + 4.48151i −2.74849
256.2 −2.03379 + 1.47763i 0.420753 + 1.29495i 1.33485 − 4.10826i 0.809017 + 0.587785i −2.76917 − 2.01192i 0.0242555 − 0.0746507i 1.80201 + 5.54603i 0.927201 − 0.673651i −2.51390
256.3 −1.69112 + 1.22867i −0.311696 − 0.959303i 0.732228 − 2.25357i 0.809017 + 0.587785i 1.70579 + 1.23933i 0.988298 − 3.04167i 0.238705 + 0.734658i 1.60394 − 1.16533i −2.09034
256.4 −1.66325 + 1.20842i 0.591107 + 1.81924i 0.688076 − 2.11768i 0.809017 + 0.587785i −3.18156 − 2.31154i −0.162490 + 0.500091i 0.143999 + 0.443184i −0.533174 + 0.387374i −2.05588
256.5 −1.59283 + 1.15726i −0.914790 − 2.81543i 0.579826 − 1.78452i 0.809017 + 0.587785i 4.71529 + 3.42586i 1.25248 − 3.85472i −0.0752260 − 0.231522i −4.66278 + 3.38771i −1.96885
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 86.15
Significant digits:
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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.e ✓ 60
11.c even 5 1 inner 935.2.u.e ✓ 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
935.2.u.e ✓ 60 1.a even 1 1 trivial
935.2.u.e ✓ 60 11.c even 5 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{60} + T_{2}^{59} + 25 T_{2}^{58} + 30 T_{2}^{57} + 391 T_{2}^{56} + 472 T_{2}^{55} + 4838 T_{2}^{54} + \cdots + 32761 \) acting on \(S_{2}^{\mathrm{new}}(935, [\chi])\). Copy content Toggle raw display