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Properties

Label 527.2.h.c
Level $527$
Weight $2$
Character orbit 527.h
Analytic conductor $4.208$
Analytic rank $0$
Dimension $96$
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] = [527,2,Mod(35,527)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(527, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("527.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 527 = 17 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 527.h (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: \(4.20811618652\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
35.1 −0.834890 − 2.56953i −0.676586 + 2.08232i −4.28739 + 3.11497i −3.73062 5.91544 −2.19901 + 1.59768i 7.21196 + 5.23979i −1.45123 − 1.05438i 3.11466 + 9.58594i
35.2 −0.824599 − 2.53786i 0.860452 − 2.64820i −4.14271 + 3.00986i −1.32092 −7.43027 0.830297 − 0.603246i 6.73700 + 4.89472i −3.84553 − 2.79394i 1.08923 + 3.35230i
35.3 −0.823486 − 2.53443i 0.190242 − 0.585506i −4.12717 + 2.99857i 2.60675 −1.64059 −1.82860 + 1.32855i 6.68649 + 4.85802i 2.12043 + 1.54058i −2.14663 − 6.60664i
35.4 −0.638967 − 1.96654i −0.842431 + 2.59274i −1.84096 + 1.33754i −1.18528 5.63700 1.46364 − 1.06340i 0.460960 + 0.334907i −3.58554 − 2.60505i 0.757352 + 2.33089i
35.5 −0.630601 − 1.94079i 0.0988673 − 0.304282i −1.75098 + 1.27216i 1.33965 −0.652894 −3.74126 + 2.71818i 0.271294 + 0.197106i 2.34424 + 1.70319i −0.844788 − 2.59999i
35.6 −0.425871 − 1.31070i −0.0626477 + 0.192810i 0.0814752 − 0.0591952i 2.62556 0.279395 2.87251 − 2.08700i −2.34217 − 1.70169i 2.39380 + 1.73920i −1.11815 − 3.44131i
35.7 −0.422745 − 1.30108i 0.656836 − 2.02153i 0.103949 − 0.0755233i −0.788591 −2.90784 2.12468 − 1.54367i −2.35573 − 1.71154i −1.22811 − 0.892277i 0.333373 + 1.02602i
35.8 −0.376285 − 1.15809i −0.0739502 + 0.227595i 0.418458 − 0.304028i −1.77800 0.291402 −0.161608 + 0.117415i −2.47981 − 1.80168i 2.38072 + 1.72969i 0.669036 + 2.05908i
35.9 −0.345717 − 1.06401i −1.04944 + 3.22986i 0.605440 − 0.439878i 0.235611 3.79941 −1.19791 + 0.870335i −2.48754 − 1.80731i −6.90361 − 5.01576i −0.0814548 − 0.250692i
35.10 −0.0792451 − 0.243891i 1.00279 − 3.08629i 1.56483 − 1.13692i 3.14033 −0.832185 −1.06954 + 0.777066i −0.816222 − 0.593020i −6.09251 − 4.42647i −0.248856 − 0.765899i
35.11 −0.0331879 − 0.102142i −0.660559 + 2.03299i 1.60870 − 1.16879i 4.10918 0.229576 −2.20537 + 1.60230i −0.346546 − 0.251781i −1.26967 − 0.922468i −0.136375 − 0.419719i
35.12 0.00688221 + 0.0211813i 0.716853 − 2.20625i 1.61763 − 1.17528i −3.45720 0.0516646 −4.04583 + 2.93947i 0.0720625 + 0.0523565i −1.92660 − 1.39976i −0.0237932 − 0.0732278i
35.13 0.0573542 + 0.176518i −0.417065 + 1.28359i 1.59016 − 1.15532i 2.24620 −0.250498 2.41959 − 1.75793i 0.595448 + 0.432618i 0.953382 + 0.692673i 0.128829 + 0.396494i
35.14 0.117984 + 0.363119i −0.485287 + 1.49356i 1.50010 − 1.08989i −2.99281 −0.599595 0.716703 − 0.520715i 1.19052 + 0.864964i 0.431836 + 0.313747i −0.353105 − 1.08675i
35.15 0.127391 + 0.392068i 0.289629 − 0.891388i 1.48055 − 1.07568i −0.351177 0.386381 1.49939 − 1.08937i 1.27737 + 0.928065i 1.71636 + 1.24701i −0.0447367 − 0.137685i
35.16 0.327429 + 1.00772i 0.722514 − 2.22367i 0.709739 − 0.515655i −0.906528 2.47741 −0.804962 + 0.584839i 2.46647 + 1.79199i −1.99563 − 1.44991i −0.296824 − 0.913529i
35.17 0.458154 + 1.41005i −0.0323158 + 0.0994577i −0.160309 + 0.116471i 1.07257 −0.155046 −2.89259 + 2.10159i 2.16125 + 1.57024i 2.41820 + 1.75693i 0.491402 + 1.51238i
35.18 0.474340 + 1.45987i −0.913245 + 2.81068i −0.288182 + 0.209377i 2.52837 −4.53641 2.31654 − 1.68306i 2.04132 + 1.48310i −4.63884 − 3.37032i 1.19931 + 3.69109i
35.19 0.664255 + 2.04437i 0.708988 − 2.18204i −2.12016 + 1.54039i 3.53489 4.93184 −0.412992 + 0.300057i −1.07936 − 0.784201i −1.83159 − 1.33073i 2.34806 + 7.22660i
35.20 0.682226 + 2.09968i 0.165718 − 0.510029i −2.32517 + 1.68934i −1.12759 1.18395 3.62195 − 2.63150i −1.56117 − 1.13426i 2.19438 + 1.59431i −0.769269 − 2.36757i
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 35.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
31.d even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 527.2.h.c ✓ 96
31.d even 5 1 inner 527.2.h.c ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
527.2.h.c ✓ 96 1.a even 1 1 trivial
527.2.h.c ✓ 96 31.d even 5 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{96} + 2 T_{2}^{95} + 41 T_{2}^{94} + 82 T_{2}^{93} + 952 T_{2}^{92} + 1812 T_{2}^{91} + \cdots + 20736 \) acting on \(S_{2}^{\mathrm{new}}(527, [\chi])\). Copy content Toggle raw display