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Properties

Label 229.2.c.a
Level $229$
Weight $2$
Character orbit 229.c
Analytic conductor $1.829$
Analytic rank $0$
Dimension $36$
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] = [229,2,Mod(94,229)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(229, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("229.94");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 229.c (of order \(3\), 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: \(1.82857420629\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 6 q^{2} - q^{3} + 22 q^{4} + 3 q^{5} + 5 q^{6} - 4 q^{7} - 18 q^{8} - 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 36 q - 6 q^{2} - q^{3} + 22 q^{4} + 3 q^{5} + 5 q^{6} - 4 q^{7} - 18 q^{8} - 13 q^{9} - 2 q^{10} - 8 q^{11} - 8 q^{12} + 12 q^{13} - 5 q^{14} + 4 q^{15} + 2 q^{16} - 6 q^{17} + 5 q^{18} - 4 q^{19} - q^{20} + 30 q^{21} - 12 q^{22} - 4 q^{23} - q^{24} - 11 q^{25} - 30 q^{26} + 2 q^{27} - 6 q^{28} + 23 q^{29} + 14 q^{30} - 7 q^{31} - 32 q^{32} - q^{33} + 2 q^{34} - 4 q^{35} + 4 q^{36} - 2 q^{37} + 12 q^{38} - 7 q^{39} + 8 q^{40} + 15 q^{41} - 16 q^{42} + 16 q^{43} + 28 q^{44} + 19 q^{45} - 11 q^{46} - q^{47} - 11 q^{48} - 20 q^{49} - 8 q^{50} + 13 q^{51} + 2 q^{52} - 38 q^{53} + 20 q^{54} - 3 q^{55} + 30 q^{56} - 52 q^{57} - 10 q^{58} - 18 q^{59} - 26 q^{60} + 12 q^{61} + 16 q^{62} - 46 q^{64} - 18 q^{65} - 4 q^{66} - 4 q^{67} - 38 q^{68} + 13 q^{69} + 37 q^{70} - 5 q^{71} - 9 q^{72} - 13 q^{73} - 62 q^{74} - 35 q^{75} - 21 q^{76} + 13 q^{77} + 6 q^{78} + 10 q^{79} - 11 q^{80} + 26 q^{81} + 33 q^{82} + 14 q^{83} - 36 q^{84} + 28 q^{85} - 8 q^{86} + 29 q^{87} - 22 q^{88} + 12 q^{89} + 9 q^{90} + q^{91} + 33 q^{92} + 12 q^{93} + 16 q^{94} + 33 q^{95} - 22 q^{96} - 21 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
94.1 −2.70298 −0.287726 + 0.498356i 5.30608 −0.151114 − 0.261736i 0.777717 − 1.34704i −2.00533 − 3.47334i −8.93627 1.33443 + 2.31130i 0.408456 + 0.707467i
94.2 −2.36743 0.726904 − 1.25903i 3.60473 −0.424686 − 0.735577i −1.72089 + 2.98068i 2.10243 + 3.64151i −3.79908 0.443221 + 0.767682i 1.00541 + 1.74143i
94.3 −2.17813 −1.14327 + 1.98021i 2.74427 1.87402 + 3.24589i 2.49020 − 4.31316i 0.892752 + 1.54629i −1.62111 −1.11415 − 1.92976i −4.08186 − 7.06999i
94.4 −1.87394 −1.48467 + 2.57153i 1.51167 −1.26275 − 2.18715i 2.78219 − 4.81889i −0.423947 − 0.734298i 0.915111 −2.90850 − 5.03766i 2.36632 + 4.09859i
94.5 −1.73801 1.40355 − 2.43102i 1.02069 −0.224942 − 0.389611i −2.43939 + 4.22515i −1.30636 − 2.26268i 1.70205 −2.43991 − 4.22604i 0.390953 + 0.677150i
94.6 −1.37750 −0.601639 + 1.04207i −0.102495 −0.0168708 − 0.0292211i 0.828758 − 1.43545i 0.234657 + 0.406438i 2.89619 0.776060 + 1.34418i 0.0232396 + 0.0402521i
94.7 −0.876607 0.238826 − 0.413658i −1.23156 0.855369 + 1.48154i −0.209356 + 0.362616i −1.23885 − 2.14575i 2.83281 1.38592 + 2.40049i −0.749823 − 1.29873i
94.8 −0.585399 1.21289 − 2.10078i −1.65731 2.10570 + 3.64719i −0.710023 + 1.22980i 2.10217 + 3.64106i 2.14099 −1.44219 − 2.49794i −1.23268 − 2.13506i
94.9 −0.584071 −0.226298 + 0.391959i −1.65886 −1.33879 − 2.31885i 0.132174 − 0.228932i 1.75061 + 3.03215i 2.13704 1.39758 + 2.42068i 0.781949 + 1.35438i
94.10 0.0804100 −1.29173 + 2.23734i −1.99353 1.82212 + 3.15600i −0.103868 + 0.179904i −1.64045 − 2.84133i −0.321120 −1.83712 − 3.18198i 0.146516 + 0.253774i
94.11 0.446057 0.621564 − 1.07658i −1.80103 −1.12121 − 1.94200i 0.277253 − 0.480216i −1.61407 − 2.79565i −1.69548 0.727316 + 1.25975i −0.500125 − 0.866242i
94.12 0.791967 −0.989721 + 1.71425i −1.37279 −1.66863 − 2.89015i −0.783826 + 1.35763i −1.73518 − 3.00543i −2.67114 −0.459094 − 0.795174i −1.32150 − 2.28890i
94.13 0.861320 −0.562529 + 0.974330i −1.25813 0.523032 + 0.905918i −0.484518 + 0.839210i 1.45932 + 2.52761i −2.80629 0.867121 + 1.50190i 0.450498 + 0.780286i
94.14 0.866017 1.41834 − 2.45663i −1.25001 −0.671198 − 1.16255i 1.22830 − 2.12748i 0.479950 + 0.831298i −2.81457 −2.52335 − 4.37057i −0.581269 − 1.00679i
94.15 1.76937 1.15577 − 2.00185i 1.13069 0.502098 + 0.869660i 2.04499 − 3.54202i 0.598403 + 1.03646i −1.53814 −1.17160 − 2.02927i 0.888400 + 1.53875i
94.16 1.97190 0.523979 − 0.907558i 1.88840 1.68150 + 2.91245i 1.03324 − 1.78962i −2.24013 − 3.88002i −0.220060 0.950892 + 1.64699i 3.31576 + 5.74307i
94.17 2.18700 −1.31639 + 2.28006i 2.78296 0.308952 + 0.535120i −2.87895 + 4.98648i 0.0827453 + 0.143319i 1.71234 −1.96577 − 3.40482i 0.675677 + 1.17031i
94.18 2.31003 0.102164 − 0.176953i 3.33624 −1.29260 − 2.23885i 0.236002 − 0.408767i 0.501290 + 0.868259i 3.08674 1.47913 + 2.56192i −2.98594 − 5.17180i
134.1 −2.70298 −0.287726 − 0.498356i 5.30608 −0.151114 + 0.261736i 0.777717 + 1.34704i −2.00533 + 3.47334i −8.93627 1.33443 − 2.31130i 0.408456 − 0.707467i
134.2 −2.36743 0.726904 + 1.25903i 3.60473 −0.424686 + 0.735577i −1.72089 − 2.98068i 2.10243 − 3.64151i −3.79908 0.443221 − 0.767682i 1.00541 − 1.74143i
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 94.18
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
229.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 229.2.c.a ✓ 36
229.c even 3 1 inner 229.2.c.a ✓ 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
229.2.c.a ✓ 36 1.a even 1 1 trivial
229.2.c.a ✓ 36 229.c even 3 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(229, [\chi])\).