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Properties

Label 667.2.g.c
Level $667$
Weight $2$
Character orbit 667.g
Analytic conductor $5.326$
Analytic rank $0$
Dimension $186$
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] = [667,2,Mod(24,667)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(667, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("667.24");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 667.g (of order \(7\), degree \(6\), 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: \(5.32602181482\)
Analytic rank: \(0\)
Dimension: \(186\)
Relative dimension: \(31\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 186 q - q^{2} - 35 q^{4} - 8 q^{5} - 12 q^{6} - 14 q^{7} + 27 q^{8} - 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 186 q - q^{2} - 35 q^{4} - 8 q^{5} - 12 q^{6} - 14 q^{7} + 27 q^{8} - 23 q^{9} - 10 q^{10} - 4 q^{11} - 24 q^{12} - 28 q^{13} - 28 q^{14} - 43 q^{16} - 28 q^{17} + 15 q^{19} - 27 q^{20} + 4 q^{21} + 36 q^{22} - 31 q^{23} - 50 q^{24} - 33 q^{25} - 15 q^{26} - 3 q^{27} + 160 q^{28} - 10 q^{29} + 54 q^{30} - 3 q^{31} - 31 q^{32} - 60 q^{33} + 7 q^{34} - 54 q^{35} - 143 q^{36} + 25 q^{37} + 125 q^{38} + 69 q^{39} + 19 q^{40} - 28 q^{41} + q^{42} + 40 q^{43} + 4 q^{44} - 20 q^{45} + 6 q^{46} - 46 q^{47} + 21 q^{48} - 101 q^{49} + 20 q^{50} - 25 q^{51} - 94 q^{52} - 16 q^{53} - 7 q^{54} + 30 q^{55} - 25 q^{56} + 120 q^{57} + 96 q^{59} - 18 q^{60} - 36 q^{61} - 113 q^{62} - 34 q^{63} - 71 q^{64} - 66 q^{65} + 181 q^{66} + 17 q^{67} + 89 q^{68} - 96 q^{70} - 51 q^{71} + 12 q^{72} + 48 q^{73} - 64 q^{74} + 428 q^{75} - 42 q^{76} + 29 q^{77} - 96 q^{78} - 50 q^{79} + 271 q^{80} - 65 q^{81} - 118 q^{82} + 54 q^{83} - 42 q^{84} - 98 q^{85} - 70 q^{86} - 46 q^{87} + 408 q^{88} - 5 q^{89} - 28 q^{90} - 32 q^{91} - 35 q^{92} + 25 q^{93} - 141 q^{94} + 60 q^{95} + 171 q^{96} + 36 q^{97} + 19 q^{98} - 4 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
24.1 −1.75958 − 2.20644i −0.390319 − 1.71010i −1.32723 + 5.81496i −1.24413 − 1.56009i −3.08644 + 3.87028i −1.02876 − 4.50730i 10.0804 − 4.85447i −0.0691904 + 0.0333203i −1.25310 + 5.49020i
24.2 −1.65426 − 2.07437i 0.365164 + 1.59989i −1.12141 + 4.91323i 1.63292 + 2.04762i 2.71469 − 3.40411i 0.562896 + 2.46621i 7.26604 − 3.49914i 0.276608 − 0.133207i 1.54625 − 6.77457i
24.3 −1.54514 − 1.93755i −0.351992 − 1.54218i −0.921582 + 4.03771i 0.403630 + 0.506135i −2.44416 + 3.06488i 0.293912 + 1.28771i 4.78164 − 2.30272i 0.448495 − 0.215984i 0.356996 − 1.56410i
24.4 −1.41910 − 1.77950i −0.0417022 − 0.182709i −0.707718 + 3.10071i −2.28341 − 2.86331i −0.265951 + 0.333492i 0.371605 + 1.62811i 2.42071 − 1.16575i 2.67126 − 1.28641i −1.85486 + 8.12665i
24.5 −1.40043 − 1.75608i 0.692708 + 3.03495i −0.677577 + 2.96866i −0.280390 − 0.351598i 4.35953 − 5.46667i −0.473419 − 2.07418i 2.11475 − 1.01841i −6.02817 + 2.90301i −0.224768 + 0.984773i
24.6 −1.39392 − 1.74793i 0.344389 + 1.50887i −0.667178 + 2.92310i 2.05139 + 2.57236i 2.15734 − 2.70521i −1.07781 − 4.72220i 2.01079 − 0.968346i 0.544828 − 0.262375i 1.63682 − 7.17136i
24.7 −1.26784 − 1.58983i −0.688651 − 3.01718i −0.475077 + 2.08145i 2.62984 + 3.29772i −3.92369 + 4.92015i −0.471172 − 2.06434i 0.247289 − 0.119088i −5.92622 + 2.85392i 1.90857 − 8.36199i
24.8 −0.980786 − 1.22987i 0.233097 + 1.02126i −0.105590 + 0.462618i −2.14631 − 2.69139i 1.02740 − 1.28832i −1.00353 − 4.39673i −2.16204 + 1.04118i 1.71426 − 0.825545i −1.20498 + 5.27936i
24.9 −0.917748 − 1.15082i 0.340560 + 1.49209i −0.0370829 + 0.162471i 0.353677 + 0.443496i 1.40458 − 1.76129i 0.0642099 + 0.281322i −2.43136 + 1.17088i 0.592554 − 0.285359i 0.185798 − 0.814036i
24.10 −0.666248 − 0.835449i −0.309201 − 1.35470i 0.190954 − 0.836623i −2.69673 − 3.38159i −0.925778 + 1.16089i 0.215153 + 0.942647i −2.75169 + 1.32514i 0.963301 − 0.463901i −1.02846 + 4.50596i
24.11 −0.647445 − 0.811871i −0.526800 − 2.30806i 0.205093 − 0.898572i 1.76661 + 2.21526i −1.53277 + 1.92204i 0.813187 + 3.56281i −2.73348 + 1.31638i −2.34673 + 1.13012i 0.654721 − 2.86852i
24.12 −0.551247 − 0.691242i −0.286405 − 1.25482i 0.271100 − 1.18777i 0.539147 + 0.676069i −0.709506 + 0.889692i −0.593437 − 2.60002i −2.56363 + 1.23458i 1.21036 − 0.582877i 0.170124 − 0.745362i
24.13 −0.288016 − 0.361161i 0.0472379 + 0.206963i 0.397558 − 1.74182i 0.362780 + 0.454912i 0.0611415 − 0.0766690i −0.838955 − 3.67570i −1.57597 + 0.758946i 2.66230 − 1.28210i 0.0598098 − 0.262044i
24.14 −0.108452 − 0.135995i 0.674171 + 2.95374i 0.438309 − 1.92036i 1.90484 + 2.38859i 0.328578 − 0.412024i 0.771751 + 3.38126i −0.622132 + 0.299603i −5.56715 + 2.68100i 0.118252 − 0.518098i
24.15 −0.106707 − 0.133807i 0.140577 + 0.615909i 0.438524 − 1.92130i −1.19595 − 1.49968i 0.0674122 − 0.0845323i 0.269633 + 1.18134i −0.612271 + 0.294854i 2.34333 − 1.12849i −0.0730502 + 0.320054i
24.16 0.0555121 + 0.0696100i 0.367429 + 1.60981i 0.443278 − 1.94213i 0.246552 + 0.309167i −0.0916623 + 0.114941i 0.595004 + 2.60688i 0.320233 − 0.154216i 0.246411 − 0.118665i −0.00783446 + 0.0343250i
24.17 0.161453 + 0.202455i 0.756037 + 3.31241i 0.430121 − 1.88448i −1.44915 − 1.81718i −0.548551 + 0.687861i −0.893629 − 3.91524i 0.917579 − 0.441883i −7.69759 + 3.70696i 0.133928 − 0.586777i
24.18 0.211076 + 0.264681i −0.688121 − 3.01485i 0.419539 − 1.83812i −1.85705 − 2.32867i 0.652729 − 0.818497i 1.02943 + 4.51022i 1.18510 − 0.570714i −5.91292 + 2.84751i 0.224376 − 0.983054i
24.19 0.629344 + 0.789172i 0.0262650 + 0.115074i 0.218323 − 0.956535i 2.37836 + 2.98236i −0.0742838 + 0.0931490i −0.591009 − 2.58938i 2.71113 − 1.30561i 2.69035 − 1.29561i −0.856795 + 3.75386i
24.20 0.691041 + 0.866538i −0.331997 − 1.45457i 0.171691 − 0.752228i −0.459614 − 0.576338i 1.03102 − 1.29286i 0.572866 + 2.50989i 2.76765 − 1.33283i 0.697346 − 0.335824i 0.181807 − 0.796547i
See next 80 embeddings (of 186 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 24.31
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.d even 7 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 667.2.g.c ✓ 186
29.d even 7 1 inner 667.2.g.c ✓ 186
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
667.2.g.c ✓ 186 1.a even 1 1 trivial
667.2.g.c ✓ 186 29.d even 7 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{186} + T_{2}^{185} + 49 T_{2}^{184} + 41 T_{2}^{183} + 1318 T_{2}^{182} + 968 T_{2}^{181} + \cdots + 1328966284864 \) acting on \(S_{2}^{\mathrm{new}}(667, [\chi])\). Copy content Toggle raw display