Properties

Label 187.2.t.a
Level 187
Weight 2
Character orbit 187.t
Analytic conductor 1.493
Analytic rank 0
Dimension 512
CM No

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Newspace parameters

Level: \( N \) = \( 187 = 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 187.t (of order \(80\) and degree \(32\))

Newform invariants

Self dual: No
Analytic conductor: \(1.4932025178\)
Analytic rank: \(0\)
Dimension: \(512\)
Relative dimension: \(16\) over \(\Q(\zeta_{80})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{80}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 512q - 40q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 40q^{6} - 40q^{7} - 40q^{8} - 24q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 512q - 40q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 40q^{6} - 40q^{7} - 40q^{8} - 24q^{9} - 40q^{11} - 16q^{12} - 56q^{14} - 24q^{15} - 40q^{17} - 80q^{18} - 40q^{19} - 24q^{20} - 48q^{22} - 48q^{23} + 80q^{24} - 40q^{25} - 56q^{26} + 48q^{27} - 40q^{28} - 40q^{29} - 40q^{30} + 40q^{31} - 64q^{34} - 80q^{35} - 56q^{36} - 56q^{37} + 80q^{38} - 40q^{39} - 40q^{40} + 80q^{41} + 72q^{42} + 32q^{44} - 64q^{45} - 40q^{46} - 24q^{47} - 72q^{48} - 88q^{49} - 40q^{51} + 240q^{52} - 24q^{53} + 128q^{55} - 64q^{56} - 40q^{57} + 88q^{58} - 88q^{59} - 152q^{60} - 40q^{61} - 40q^{62} + 80q^{63} - 88q^{64} + 408q^{66} - 40q^{68} + 192q^{69} - 168q^{70} - 24q^{71} - 40q^{72} - 40q^{73} - 40q^{74} - 88q^{75} + 192q^{77} - 64q^{78} - 40q^{79} + 248q^{80} - 40q^{81} - 24q^{82} - 40q^{85} - 112q^{86} + 128q^{88} - 64q^{89} - 40q^{90} + 56q^{91} + 136q^{92} - 88q^{93} + 440q^{94} - 40q^{95} - 40q^{96} - 88q^{97} + 72q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
6.1 −2.62383 0.206500i 0.338932 + 0.156250i 4.86645 + 0.770770i 2.42091 + 3.07091i −0.857033 0.479962i −0.252119 + 0.683399i −7.49112 1.79846i −1.85788 2.17530i −5.71790 8.55745i
6.2 −2.59078 0.203899i −2.26719 1.04519i 4.69518 + 0.743644i −1.25029 1.58598i 5.66068 + 3.17014i 1.40072 3.79682i −6.95859 1.67061i 2.09940 + 2.45808i 2.91584 + 4.36387i
6.3 −2.09150 0.164604i 0.560652 + 0.258464i 2.37189 + 0.375671i −1.69373 2.14848i −1.13006 0.632864i −0.674528 + 1.82839i −0.818977 0.196619i −1.70082 1.99140i 3.18878 + 4.77235i
6.4 −1.75467 0.138096i 2.81986 + 1.29997i 1.08442 + 0.171756i 0.649663 + 0.824093i −4.76840 2.67043i 1.37212 3.71929i 1.54385 + 0.370644i 4.31333 + 5.05026i −1.02614 1.53573i
6.5 −1.67599 0.131903i −1.59616 0.735838i 0.816165 + 0.129268i 0.713695 + 0.905318i 2.57808 + 1.44380i −1.01149 + 2.74177i 1.91861 + 0.460617i 0.0579148 + 0.0678096i −1.07673 1.61144i
6.6 −1.06157 0.0835470i −2.09399 0.965344i −0.855435 0.135488i −0.686188 0.870426i 2.14226 + 1.19972i 0.248365 0.673223i 2.96763 + 0.712466i 1.50457 + 1.76163i 0.655712 + 0.981343i
6.7 −0.877055 0.0690257i 2.14542 + 0.989054i −1.21092 0.191790i 0.214388 + 0.271950i −1.81338 1.01554i −1.45693 + 3.94919i 2.75972 + 0.662550i 1.67627 + 1.96266i −0.169259 0.253314i
6.8 −0.426567 0.0335715i −0.467735 0.215629i −1.79454 0.284228i 1.12229 + 1.42362i 0.192281 + 0.107683i 1.60101 4.33973i 1.58808 + 0.381264i −1.77606 2.07950i −0.430939 0.644946i
6.9 −0.213005 0.0167639i 1.15403 + 0.532014i −1.93029 0.305727i −2.42133 3.07145i −0.236896 0.132668i 0.704712 1.91021i 0.821557 + 0.197238i −0.899602 1.05330i 0.464268 + 0.694826i
6.10 0.540115 + 0.0425079i −1.09908 0.506683i −1.68546 0.266951i −0.995194 1.26240i −0.572092 0.320387i −0.583247 + 1.58096i −1.95262 0.468784i −0.997093 1.16745i −0.483857 0.724143i
6.11 0.629923 + 0.0495761i 1.56161 + 0.719913i −1.58103 0.250411i 2.34147 + 2.97014i 0.948006 + 0.530909i −0.248193 + 0.672757i −2.21234 0.531136i −0.0279848 0.0327660i 1.32770 + 1.98704i
6.12 0.659382 + 0.0518945i −2.80529 1.29326i −1.54329 0.244432i 2.38463 + 3.02489i −1.78264 0.998329i −0.787459 + 2.13450i −2.29122 0.550073i 4.24880 + 4.97470i 1.41541 + 2.11831i
6.13 1.51646 + 0.119348i 1.78375 + 0.822318i 0.310038 + 0.0491051i −0.164969 0.209262i 2.60684 + 1.45990i 0.694532 1.88261i −2.49394 0.598743i 0.557198 + 0.652395i −0.225194 0.337026i
6.14 1.93716 + 0.152458i −2.58853 1.19333i 1.75398 + 0.277804i −2.16149 2.74184i −4.83248 2.70632i 0.639914 1.73456i −0.423527 0.101680i 3.32813 + 3.89674i −3.76915 5.64093i
6.15 2.13560 + 0.168075i 0.194323 + 0.0895840i 2.55715 + 0.405012i 0.179483 + 0.227673i 0.399938 + 0.223976i −0.474986 + 1.28751i 1.22694 + 0.294561i −1.91861 2.24640i 0.345037 + 0.516384i
6.16 2.39250 + 0.188294i −1.45628 0.671356i 3.71324 + 0.588119i 1.43760 + 1.82358i −3.35775 1.88043i 0.0778254 0.210955i 4.10601 + 0.985766i −0.278301 0.325848i 3.09608 + 4.63362i
7.1 −1.38079 2.25324i 0.273940 + 0.347491i −2.26253 + 4.44046i 0.237290 + 0.219348i 0.404728 1.09706i 0.586843 + 4.95822i 7.86045 0.618631i 0.654629 2.72673i 0.166598 0.837543i
7.2 −1.18360 1.93146i −0.181018 0.229620i −1.42165 + 2.79015i 2.86138 + 2.64503i −0.229250 + 0.621408i −0.444980 3.75961i 2.55516 0.201096i 0.680378 2.83398i 1.72204 8.65730i
7.3 −0.987367 1.61124i 1.05876 + 1.34304i −0.713210 + 1.39975i −2.47426 2.28718i 1.11856 3.03199i −0.0495816 0.418913i −0.808223 + 0.0636085i 0.0175722 0.0731935i −1.24219 + 6.24491i
7.4 −0.917683 1.49752i −0.728333 0.923886i −0.492452 + 0.966491i −0.908277 0.839602i −0.715161 + 1.93853i −0.0328041 0.277160i −1.60259 + 0.126126i 0.377240 1.57132i −0.423813 + 2.13065i
See next 80 embeddings (of 512 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 184.16
Significant digits:
Format:

Inner twists

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

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(187, [\chi])\).