Properties

Label 945.2.cs.b
Level 945
Weight 2
Character orbit 945.cs
Analytic conductor 7.546
Analytic rank 0
Dimension 816
CM No

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Newspace parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 945.cs (of order \(18\) and degree \(6\))

Newform invariants

Self dual: No
Analytic conductor: \(7.54586299101\)
Analytic rank: \(0\)
Dimension: \(816\)
Relative dimension: \(136\) over \(\Q(\zeta_{18})\)
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.

\(\operatorname{Tr}(f)(q) = \) \(816q \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(816q \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 78q^{30} \) \(\mathstrut -\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut -\mathstrut 84q^{39} \) \(\mathstrut -\mathstrut 36q^{44} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 24q^{50} \) \(\mathstrut -\mathstrut 60q^{51} \) \(\mathstrut +\mathstrut 120q^{56} \) \(\mathstrut -\mathstrut 150q^{60} \) \(\mathstrut -\mathstrut 444q^{64} \) \(\mathstrut +\mathstrut 162q^{65} \) \(\mathstrut +\mathstrut 21q^{70} \) \(\mathstrut -\mathstrut 36q^{71} \) \(\mathstrut -\mathstrut 48q^{74} \) \(\mathstrut -\mathstrut 48q^{79} \) \(\mathstrut -\mathstrut 48q^{81} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut -\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 192q^{86} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 210q^{95} \) \(\mathstrut -\mathstrut 216q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
104.1 −2.58909 0.942353i −0.600558 + 1.62460i 4.28329 + 3.59410i 1.90382 + 1.17280i 3.08585 3.64031i −0.535422 + 2.59101i −4.94766 8.56959i −2.27866 1.95133i −3.82398 4.83056i
104.2 −2.58909 0.942353i 0.600558 1.62460i 4.28329 + 3.59410i −1.90382 1.17280i −3.08585 + 3.64031i 2.64462 0.0773642i −4.94766 8.56959i −2.27866 1.95133i 3.82398 + 4.83056i
104.3 −2.53031 0.920958i −1.72154 0.190516i 4.02222 + 3.37504i 0.693777 2.12572i 4.18058 + 2.06753i −0.625891 + 2.57065i −4.37650 7.58031i 2.92741 + 0.655961i −3.71317 + 4.73979i
104.4 −2.53031 0.920958i 1.72154 + 0.190516i 4.02222 + 3.37504i −0.693777 + 2.12572i −4.18058 2.06753i 2.64028 0.169993i −4.37650 7.58031i 2.92741 + 0.655961i 3.71317 4.73979i
104.5 −2.50242 0.910806i −0.792257 + 1.54024i 3.90044 + 3.27286i −0.778079 2.09633i 3.38541 3.13272i 1.23163 2.34160i −4.11657 7.13012i −1.74466 2.44053i 0.0377315 + 5.95457i
104.6 −2.50242 0.910806i 0.792257 1.54024i 3.90044 + 3.27286i 0.778079 + 2.09633i −3.38541 + 3.13272i −2.51990 + 0.806302i −4.11657 7.13012i −1.74466 2.44053i −0.0377315 5.95457i
104.7 −2.39005 0.869908i −0.413843 1.68188i 3.42352 + 2.87268i 1.33788 1.79167i −0.473977 + 4.37980i −2.12702 1.57346i −3.14000 5.43864i −2.65747 + 1.39207i −4.75619 + 3.11835i
104.8 −2.39005 0.869908i 0.413843 + 1.68188i 3.42352 + 2.87268i −1.33788 + 1.79167i 0.473977 4.37980i −1.18021 2.36793i −3.14000 5.43864i −2.65747 + 1.39207i 4.75619 3.11835i
104.9 −2.37527 0.864529i −1.19353 1.25518i 3.36242 + 2.82141i 2.05172 + 0.889078i 1.74982 + 4.01325i 2.60397 0.468317i −3.01977 5.23040i −0.150973 + 2.99620i −4.10475 3.88557i
104.10 −2.37527 0.864529i 1.19353 + 1.25518i 3.36242 + 2.82141i −2.05172 0.889078i −1.74982 4.01325i −0.913378 + 2.48309i −3.01977 5.23040i −0.150973 + 2.99620i 4.10475 + 3.88557i
104.11 −2.30468 0.838835i −1.61471 + 0.626663i 3.07581 + 2.58091i −1.65639 + 1.50213i 4.24706 0.0897813i 2.42327 + 1.06196i −2.47122 4.28027i 2.21459 2.02376i 5.07748 2.07249i
104.12 −2.30468 0.838835i 1.61471 0.626663i 3.07581 + 2.58091i 1.65639 1.50213i −4.24706 + 0.0897813i 0.625030 + 2.57086i −2.47122 4.28027i 2.21459 2.02376i −5.07748 + 2.07249i
104.13 −2.27225 0.827033i −1.72657 + 0.137621i 2.94706 + 2.47288i 1.34694 + 1.78487i 4.03703 + 1.11522i −1.82568 1.91491i −2.23324 3.86809i 2.96212 0.475226i −1.58445 5.16963i
104.14 −2.27225 0.827033i 1.72657 0.137621i 2.94706 + 2.47288i −1.34694 1.78487i −4.03703 1.11522i −1.56879 2.13047i −2.23324 3.86809i 2.96212 0.475226i 1.58445 + 5.16963i
104.15 −2.19076 0.797371i −0.522216 1.65145i 2.63153 + 2.20812i −2.22823 0.187052i −0.172770 + 4.03433i −0.716428 + 2.54691i −1.67300 2.89773i −2.45458 + 1.72483i 4.73236 + 2.18651i
104.16 −2.19076 0.797371i 0.522216 + 1.65145i 2.63153 + 2.20812i 2.22823 + 0.187052i 0.172770 4.03433i 2.63262 0.263278i −1.67300 2.89773i −2.45458 + 1.72483i −4.73236 2.18651i
104.17 −2.05378 0.747516i −1.57383 + 0.723218i 2.12716 + 1.78490i 1.84479 1.26363i 3.77293 0.308866i −0.111990 2.64338i −0.848890 1.47032i 1.95391 2.27645i −4.73338 + 1.21621i
104.18 −2.05378 0.747516i 1.57383 0.723218i 2.12716 + 1.78490i −1.84479 + 1.26363i −3.77293 + 0.308866i −2.58377 0.569307i −0.848890 1.47032i 1.95391 2.27645i 4.73338 1.21621i
104.19 −1.96750 0.716110i −1.00171 + 1.41301i 1.82614 + 1.53231i −1.23328 + 1.86521i 2.98272 2.06275i −2.38678 + 1.14161i −0.401851 0.696026i −0.993173 2.83083i 3.76217 2.78664i
104.20 −1.96750 0.716110i 1.00171 1.41301i 1.82614 + 1.53231i 1.23328 1.86521i −2.98272 + 2.06275i 1.53873 2.15228i −0.401851 0.696026i −0.993173 2.83083i −3.76217 + 2.78664i
See next 80 embeddings (of 816 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 839.136
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{408} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(945, [\chi])\).