Properties

Label 201.3.n.a
Level 201
Weight 3
Character orbit 201.n
Analytic conductor 5.477
Analytic rank 0
Dimension 220
CM No

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Newspace parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 201.n (of order \(66\) and degree \(20\))

Newform invariants

Self dual: No
Analytic conductor: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(220\)
Relative dimension: \(11\) over \(\Q(\zeta_{66})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 220q - 26q^{4} + 33q^{6} + 15q^{7} - 33q^{8} + 66q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 220q - 26q^{4} + 33q^{6} + 15q^{7} - 33q^{8} + 66q^{9} + 93q^{10} + 69q^{11} - 21q^{12} + 27q^{13} - 6q^{14} - 27q^{15} + 58q^{16} + 8q^{17} + 54q^{19} + 12q^{20} + 15q^{21} - 69q^{22} - 164q^{23} + 56q^{25} - 71q^{26} + 152q^{28} - 119q^{29} - 18q^{30} - 76q^{31} - 676q^{32} - 30q^{33} + 24q^{34} + 327q^{35} - 21q^{36} + 86q^{37} - 108q^{38} - 27q^{39} - 115q^{40} - 6q^{41} + 132q^{42} - 385q^{43} - 189q^{44} + 541q^{46} + 794q^{47} + 174q^{48} + 40q^{49} - 714q^{50} - 240q^{51} + 924q^{52} - 748q^{53} + 355q^{55} - 899q^{56} + 195q^{57} - 1672q^{58} - 466q^{59} - 516q^{60} - 217q^{61} - 818q^{62} + 219q^{63} + 691q^{64} - 68q^{65} - 72q^{67} - 198q^{68} + 69q^{69} - 44q^{70} + 481q^{71} + 264q^{72} - 1458q^{73} + 703q^{74} + 396q^{75} + 1270q^{76} + 1096q^{77} + 741q^{78} - 89q^{79} + 3363q^{80} - 198q^{81} - 28q^{82} + 1023q^{83} + 321q^{84} - 237q^{85} + 329q^{86} + 126q^{87} + 1768q^{88} - 1409q^{89} - 279q^{90} + 916q^{91} - 1340q^{92} + 177q^{93} - 1144q^{94} - 357q^{95} + 105q^{96} + 441q^{97} + 397q^{98} + 90q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
7.1 −1.59491 3.09369i 0.487975 1.66189i −4.70694 + 6.60997i 1.53724 + 1.33203i −5.91964 + 1.14092i −7.89972 0.376310i 14.1756 + 2.03814i −2.52376 1.62192i 1.66912 6.88019i
7.2 −1.30082 2.52324i 0.487975 1.66189i −2.35436 + 3.30624i 4.87030 + 4.22014i −4.82811 + 0.930542i 4.14875 + 0.197629i 0.165362 + 0.0237755i −2.52376 1.62192i 4.31303 17.7785i
7.3 −1.00055 1.94079i 0.487975 1.66189i −0.445350 + 0.625406i −2.50061 2.16679i −3.71363 + 0.715743i −2.72019 0.129579i −6.98581 1.00441i −2.52376 1.62192i −1.70331 + 7.02114i
7.4 −0.781729 1.51634i 0.487975 1.66189i 0.632031 0.887563i −5.35383 4.63912i −2.90146 + 0.559211i 5.80206 + 0.276386i −8.59443 1.23569i −2.52376 1.62192i −2.84925 + 11.7448i
7.5 −0.180828 0.350757i 0.487975 1.66189i 2.22990 3.13145i −1.23290 1.06831i −0.671158 + 0.129355i −12.1138 0.577054i −3.06404 0.440542i −2.52376 1.62192i −0.151776 + 0.625628i
7.6 −0.131330 0.254745i 0.487975 1.66189i 2.27258 3.19139i 4.91546 + 4.25927i −0.487444 + 0.0939471i 9.56392 + 0.455585i −2.24620 0.322955i −2.52376 1.62192i 0.439479 1.81156i
7.7 0.379014 + 0.735185i 0.487975 1.66189i 1.92338 2.70101i −0.796867 0.690489i 1.40675 0.271128i 0.460255 + 0.0219247i 5.98959 + 0.861173i −2.52376 1.62192i 0.205613 0.847550i
7.8 1.06534 + 2.06647i 0.487975 1.66189i −0.815135 + 1.14470i 6.29564 + 5.45520i 3.95411 0.762093i −3.64687 0.173722i 5.97115 + 0.858522i −2.52376 1.62192i −4.56603 + 18.8214i
7.9 1.24209 + 2.40933i 0.487975 1.66189i −1.94183 + 2.72692i −3.49385 3.02744i 4.61015 0.888533i 12.8945 + 0.614243i 1.75028 + 0.251652i −2.52376 1.62192i 2.95440 12.1782i
7.10 1.33922 + 2.59772i 0.487975 1.66189i −2.63440 + 3.69950i −6.93647 6.01049i 4.97062 0.958009i −12.6927 0.604627i −1.56684 0.225278i −2.52376 1.62192i 6.32410 26.0683i
7.11 1.65710 + 3.21433i 0.487975 1.66189i −5.26571 + 7.39465i 2.82046 + 2.44394i 6.15049 1.18541i 1.70167 + 0.0810603i −18.1765 2.61339i −2.52376 1.62192i −3.18185 + 13.1158i
13.1 −2.38627 3.03439i 1.30900 + 1.13425i −2.57021 + 10.5945i −2.16084 3.36234i 0.318143 6.67865i 1.54810 3.86696i 24.2354 11.0680i 0.426945 + 2.96946i −5.04629 + 14.5803i
13.2 −1.93043 2.45475i 1.30900 + 1.13425i −1.35617 + 5.59021i 2.11556 + 3.29187i 0.257370 5.40286i 0.841588 2.10218i 4.97788 2.27332i 0.426945 + 2.96946i 3.99677 11.5479i
13.3 −1.54479 1.96435i 1.30900 + 1.13425i −0.529291 + 2.18177i 1.33314 + 2.07440i 0.205954 4.32351i 1.17385 2.93213i −3.98931 + 1.82186i 0.426945 + 2.96946i 2.01545 5.82326i
13.4 −1.30496 1.65939i 1.30900 + 1.13425i −0.107628 + 0.443649i −3.81619 5.93810i 0.173980 3.65230i −4.15363 + 10.3753i −6.80446 + 3.10749i 0.426945 + 2.96946i −4.87367 + 14.0816i
13.5 −0.377872 0.480504i 1.30900 + 1.13425i 0.854939 3.52411i −1.13061 1.75926i 0.0503788 1.05758i 3.34306 8.35055i −4.24059 + 1.93661i 0.426945 + 2.96946i −0.418106 + 1.20804i
13.6 −0.228760 0.290892i 1.30900 + 1.13425i 0.910749 3.75416i 3.04344 + 4.73569i 0.0304988 0.640249i −3.81167 + 9.52110i −2.64690 + 1.20880i 0.426945 + 2.96946i 0.681358 1.96865i
13.7 0.929003 + 1.18132i 1.30900 + 1.13425i 0.410557 1.69234i −4.88137 7.59556i −0.123857 + 2.60007i −0.164363 + 0.410559i 7.84879 3.58442i 0.426945 + 2.96946i 4.43800 12.8228i
13.8 0.953733 + 1.21277i 1.30900 + 1.13425i 0.381831 1.57393i 5.07833 + 7.90204i −0.127154 + 2.66929i 0.437890 1.09380i 7.88672 3.60174i 0.426945 + 2.96946i −4.73999 + 13.6953i
13.9 1.03156 + 1.31174i 1.30900 + 1.13425i 0.286498 1.18096i 0.446140 + 0.694208i −0.137530 + 2.88711i 2.69847 6.74045i 7.91651 3.61535i 0.426945 + 2.96946i −0.450398 + 1.30134i
See next 80 embeddings (of 220 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 184.11
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 \(T_{2}^{220} + \cdots\) acting on \(S_{3}^{\mathrm{new}}(201, [\chi])\).