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Properties

Label 567.2.bd.a
Level $567$
Weight $2$
Character orbit 567.bd
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.bd (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 132q + 3q^{2} - 3q^{4} + 9q^{5} - 6q^{7} + 18q^{8} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 132q + 3q^{2} - 3q^{4} + 9q^{5} - 6q^{7} + 18q^{8} - 9q^{10} - 9q^{11} + 42q^{14} - 15q^{16} + 9q^{17} - 9q^{19} + 18q^{20} - 12q^{22} - 30q^{23} - 3q^{25} - 12q^{28} - 6q^{29} - 9q^{31} + 51q^{32} + 18q^{34} + 9q^{35} - 6q^{37} + 9q^{38} - 9q^{40} - 12q^{43} - 6q^{46} - 45q^{47} + 30q^{49} + 9q^{50} - 9q^{52} - 45q^{53} + 51q^{56} - 3q^{58} + 9q^{59} - 63q^{61} - 99q^{62} + 18q^{64} + 102q^{65} - 3q^{67} - 144q^{68} - 15q^{70} - 18q^{71} + 33q^{74} - 36q^{76} + 57q^{77} - 21q^{79} + 72q^{80} - 18q^{82} - 90q^{83} + 9q^{85} + 33q^{86} + 45q^{88} + 9q^{89} - 21q^{91} - 150q^{92} - 9q^{94} - 27q^{95} + 180q^{98} + O(q^{100}) \)

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.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 −2.50283 + 0.441316i 0 4.19001 − 1.52504i 0.437341 − 0.159179i 0 −1.48170 + 2.19193i −5.41196 + 3.12460i 0 −1.02434 + 0.591403i
17.2 −2.45739 + 0.433304i 0 3.97163 − 1.44555i 0.335948 − 0.122275i 0 0.0666399 − 2.64491i −4.81149 + 2.77792i 0 −0.772573 + 0.446045i
17.3 −2.22112 + 0.391643i 0 2.90060 − 1.05573i 3.20807 − 1.16764i 0 −2.62457 − 0.334082i −2.12267 + 1.22552i 0 −6.66821 + 3.84989i
17.4 −1.87320 + 0.330296i 0 1.52040 − 0.553380i 0.848304 − 0.308757i 0 2.48993 + 0.894564i 0.629295 − 0.363324i 0 −1.48706 + 0.858555i
17.5 −1.66985 + 0.294440i 0 0.822331 − 0.299304i −1.39543 + 0.507895i 0 −0.356869 − 2.62157i 1.65184 − 0.953692i 0 2.18062 − 1.25898i
17.6 −1.65422 + 0.291684i 0 0.771989 − 0.280981i −3.52188 + 1.28186i 0 −2.17331 + 1.50888i 1.71431 − 0.989760i 0 5.45209 − 3.14776i
17.7 −1.10401 + 0.194666i 0 −0.698446 + 0.254214i 3.85196 − 1.40200i 0 2.61259 − 0.417595i 2.66330 − 1.53766i 0 −3.97967 + 2.29767i
17.8 −0.892534 + 0.157378i 0 −1.10754 + 0.403110i 1.14226 − 0.415747i 0 −1.98483 + 1.74942i 2.49483 − 1.44039i 0 −0.954073 + 0.550834i
17.9 −0.882178 + 0.155552i 0 −1.12534 + 0.409592i −0.123522 + 0.0449584i 0 1.69913 + 2.02805i 2.48059 − 1.43217i 0 0.101975 − 0.0588754i
17.10 −0.245063 + 0.0432112i 0 −1.82120 + 0.662861i −1.99870 + 0.727467i 0 0.302346 − 2.62842i 0.848674 − 0.489982i 0 0.458373 − 0.264642i
17.11 −0.0159182 + 0.00280680i 0 −1.87914 + 0.683951i −3.75147 + 1.36542i 0 0.157938 + 2.64103i 0.0559891 − 0.0323253i 0 0.0558840 − 0.0322646i
17.12 0.0147002 − 0.00259205i 0 −1.87918 + 0.683964i −1.54651 + 0.562885i 0 2.21011 − 1.45445i −0.0517058 + 0.0298524i 0 −0.0212751 + 0.0122832i
17.13 0.313923 − 0.0553531i 0 −1.78390 + 0.649287i 2.68563 − 0.977491i 0 −2.48320 − 0.913082i −1.07619 + 0.621337i 0 0.788975 − 0.455515i
17.14 0.877614 − 0.154747i 0 −1.13313 + 0.412424i 1.30288 − 0.474210i 0 1.81190 + 1.92796i −2.47415 + 1.42845i 0 1.07004 − 0.617790i
17.15 0.910598 − 0.160563i 0 −1.07598 + 0.391623i 0.473927 − 0.172495i 0 −2.46079 − 0.971863i −2.51844 + 1.45402i 0 0.403861 − 0.233169i
17.16 1.38665 − 0.244504i 0 −0.0163608 + 0.00595485i −1.98299 + 0.721749i 0 −2.18605 − 1.49037i −2.46004 + 1.42030i 0 −2.57325 + 1.48566i
17.17 1.57155 − 0.277106i 0 0.513586 − 0.186930i −1.78318 + 0.649025i 0 −1.28547 + 2.31248i −2.00866 + 1.15970i 0 −2.62250 + 1.51410i
17.18 1.63190 − 0.287749i 0 0.700923 − 0.255115i 3.60525 − 1.31220i 0 2.03118 − 1.69538i −1.79971 + 1.03907i 0 5.50583 − 3.17879i
17.19 2.06025 − 0.363278i 0 2.23328 − 0.812849i −0.338534 + 0.123216i 0 1.84499 − 1.89632i 0.682329 − 0.393943i 0 −0.652704 + 0.376839i
17.20 2.26715 − 0.399760i 0 3.10078 − 1.12859i 1.73217 − 0.630457i 0 0.678971 + 2.55715i 2.59137 − 1.49613i 0 3.67505 − 2.12179i
See next 80 embeddings (of 132 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 467.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
189.bd even 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 567.2.bd.a 132
3.b odd 2 1 189.2.bd.a yes 132
7.d odd 6 1 567.2.ba.a 132
21.g even 6 1 189.2.ba.a ✓ 132
27.e even 9 1 189.2.ba.a ✓ 132
27.f odd 18 1 567.2.ba.a 132
189.z odd 18 1 189.2.bd.a yes 132
189.bd even 18 1 inner 567.2.bd.a 132
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
189.2.ba.a ✓ 132 21.g even 6 1
189.2.ba.a ✓ 132 27.e even 9 1
189.2.bd.a yes 132 3.b odd 2 1
189.2.bd.a yes 132 189.z odd 18 1
567.2.ba.a 132 7.d odd 6 1
567.2.ba.a 132 27.f odd 18 1
567.2.bd.a 132 1.a even 1 1 trivial
567.2.bd.a 132 189.bd even 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(567, [\chi])\).