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Properties

Label 229.3.d.a
Level $229$
Weight $3$
Character orbit 229.d
Analytic conductor $6.240$
Analytic rank $0$
Dimension $76$
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] = [229,3,Mod(107,229)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(229, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("229.107");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 229 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 229.d (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: \(6.23979805385\)
Analytic rank: \(0\)
Dimension: \(76\)
Relative dimension: \(38\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 76 q - 4 q^{3} - 6 q^{6} - 18 q^{7} - 6 q^{8} + 204 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 76 q - 4 q^{3} - 6 q^{6} - 18 q^{7} - 6 q^{8} + 204 q^{9} + 2 q^{10} - 72 q^{13} - 20 q^{14} - 228 q^{16} - 40 q^{17} + 36 q^{18} - 40 q^{19} - 20 q^{20} - 98 q^{21} + 6 q^{22} - 8 q^{23} + 70 q^{24} - 268 q^{25} - 100 q^{27} - 88 q^{28} - 64 q^{29} + 144 q^{30} + 6 q^{31} + 16 q^{32} - 38 q^{34} + 50 q^{35} + 76 q^{37} + 192 q^{38} + 36 q^{39} - 82 q^{40} - 68 q^{41} + 292 q^{42} + 84 q^{43} + 108 q^{44} + 164 q^{47} - 284 q^{48} - 36 q^{50} - 152 q^{51} + 670 q^{52} - 404 q^{53} - 466 q^{54} + 16 q^{55} + 56 q^{57} + 8 q^{59} + 1148 q^{60} - 128 q^{61} - 156 q^{63} + 76 q^{65} + 384 q^{66} + 14 q^{67} - 418 q^{69} - 662 q^{72} + 186 q^{73} - 78 q^{74} + 124 q^{75} + 154 q^{77} - 142 q^{79} + 228 q^{81} - 72 q^{82} + 212 q^{83} - 1034 q^{84} - 26 q^{86} + 554 q^{87} + 160 q^{88} + 110 q^{89} - 226 q^{90} + 588 q^{91} - 262 q^{92} - 602 q^{93} + 568 q^{94} + 1380 q^{96} - 854 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
107.1 −2.81685 + 2.81685i 3.27192 − 11.8693i 2.79051i −9.21650 + 9.21650i −7.54814 − 7.54814i 22.1666 + 22.1666i 1.70544 −7.86046 − 7.86046i
107.2 −2.64585 + 2.64585i −1.58050 − 10.0010i − 5.11440i 4.18177 − 4.18177i 7.08910 + 7.08910i 15.8778 + 15.8778i −6.50201 13.5319 + 13.5319i
107.3 −2.30216 + 2.30216i −1.62543 − 6.59986i 3.18425i 3.74201 − 3.74201i −0.719195 − 0.719195i 5.98530 + 5.98530i −6.35796 −7.33064 − 7.33064i
107.4 −2.29851 + 2.29851i −2.52032 − 6.56633i 8.44172i 5.79298 − 5.79298i 1.93663 + 1.93663i 5.89874 + 5.89874i −2.64800 −19.4034 − 19.4034i
107.5 −2.27163 + 2.27163i 2.26763 − 6.32063i − 3.00083i −5.15123 + 5.15123i 0.305279 + 0.305279i 5.27163 + 5.27163i −3.85784 6.81679 + 6.81679i
107.6 −2.21815 + 2.21815i −3.04728 − 5.84038i − 8.86409i 6.75932 − 6.75932i −8.34005 − 8.34005i 4.08224 + 4.08224i 0.285892 19.6619 + 19.6619i
107.7 −2.15876 + 2.15876i 4.72713 − 5.32052i 4.01187i −10.2048 + 10.2048i 6.84371 + 6.84371i 2.85069 + 2.85069i 13.3457 −8.66069 − 8.66069i
107.8 −1.86235 + 1.86235i −5.28421 − 2.93670i 2.50053i 9.84104 − 9.84104i −3.04352 − 3.04352i −1.98025 − 1.98025i 18.9228 −4.65686 − 4.65686i
107.9 −1.70624 + 1.70624i −5.19839 − 1.82248i − 4.08566i 8.86968 − 8.86968i 9.45555 + 9.45555i −3.71536 − 3.71536i 18.0233 6.97111 + 6.97111i
107.10 −1.68183 + 1.68183i 5.69061 − 1.65711i − 6.22651i −9.57064 + 9.57064i −7.49629 − 7.49629i −3.94034 − 3.94034i 23.3830 10.4719 + 10.4719i
107.11 −1.41814 + 1.41814i 1.16808 − 0.0222196i − 4.84850i −1.65650 + 1.65650i 1.66603 + 1.66603i −5.64103 − 5.64103i −7.63559 6.87584 + 6.87584i
107.12 −1.36286 + 1.36286i 1.54995 0.285242i 7.72827i −2.11236 + 2.11236i −7.81105 − 7.81105i −5.84017 − 5.84017i −6.59766 −10.5325 − 10.5325i
107.13 −1.31348 + 1.31348i 1.78248 0.549536i − 2.52274i −2.34125 + 2.34125i 0.0330039 + 0.0330039i −5.97573 − 5.97573i −5.82276 3.31357 + 3.31357i
107.14 −0.975070 + 0.975070i −3.21946 2.09848i 0.620030i 3.13920 − 3.13920i −4.41301 − 4.41301i −5.94644 − 5.94644i 1.36494 −0.604573 − 0.604573i
107.15 −0.849353 + 0.849353i −0.0343079 2.55720i 6.66228i 0.0291395 − 0.0291395i 9.07595 + 9.07595i −5.56937 − 5.56937i −8.99882 −5.65862 − 5.65862i
107.16 −0.567480 + 0.567480i −3.30818 3.35593i − 4.93412i 1.87733 − 1.87733i 2.30231 + 2.30231i −4.17435 − 4.17435i 1.94404 2.80001 + 2.80001i
107.17 −0.500959 + 0.500959i 4.95337 3.49808i 4.01949i −2.48144 + 2.48144i −1.22690 − 1.22690i −3.75623 − 3.75623i 15.5359 −2.01360 − 2.01360i
107.18 −0.132366 + 0.132366i 3.73689 3.96496i − 8.10000i −0.494638 + 0.494638i 7.72510 + 7.72510i −1.05429 − 1.05429i 4.96435 1.07217 + 1.07217i
107.19 0.0115873 − 0.0115873i −4.59927 3.99973i 7.24170i −0.0532931 + 0.0532931i 1.30824 + 1.30824i 0.0926952 + 0.0926952i 12.1533 0.0839116 + 0.0839116i
107.20 0.0970443 − 0.0970443i 0.832767 3.98116i − 4.77079i 0.0808153 − 0.0808153i −8.21099 − 8.21099i 0.774527 + 0.774527i −8.30650 −0.462978 − 0.462978i
See all 76 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 107.38
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
229.d odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 229.3.d.a ✓ 76
229.d odd 4 1 inner 229.3.d.a ✓ 76
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
229.3.d.a ✓ 76 1.a even 1 1 trivial
229.3.d.a ✓ 76 229.d odd 4 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(229, [\chi])\).