Properties

Label 201.4.i.a
Level 201
Weight 4
Character orbit 201.i
Analytic conductor 11.859
Analytic rank 0
Dimension 170
CM No

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Newspace parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 201.i (of order \(11\) and degree \(10\))

Newform invariants

Self dual: No
Analytic conductor: \(11.8593839112\)
Analytic rank: \(0\)
Dimension: \(170\)
Relative dimension: \(17\) over \(\Q(\zeta_{11})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 170q + 2q^{2} - 51q^{3} - 82q^{4} + 4q^{5} - 27q^{6} - 16q^{7} - 177q^{8} - 153q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 170q + 2q^{2} - 51q^{3} - 82q^{4} + 4q^{5} - 27q^{6} - 16q^{7} - 177q^{8} - 153q^{9} + 49q^{10} + 144q^{11} - 81q^{12} + 20q^{13} - 146q^{14} - 54q^{15} - 458q^{16} + 38q^{17} + 18q^{18} + 152q^{19} + 284q^{20} - 48q^{21} + 133q^{22} + 366q^{23} + 162q^{24} - 333q^{25} - 220q^{26} - 459q^{27} + 1621q^{28} - 1448q^{29} - 414q^{30} - 670q^{31} - 301q^{32} + 234q^{33} + 78q^{34} + 1476q^{35} - 243q^{36} - 3030q^{37} - 356q^{38} + 60q^{39} + 637q^{40} - 882q^{41} - 1098q^{42} + 2702q^{43} - 951q^{44} + 36q^{45} - 483q^{46} + 776q^{47} - 1374q^{48} + 1433q^{49} + 3267q^{50} + 378q^{51} + 4474q^{52} + 2840q^{53} + 54q^{54} + 1982q^{55} + 3828q^{56} + 489q^{57} + 1740q^{58} - 1136q^{59} - 3339q^{60} - 868q^{61} + 452q^{62} + 1341q^{63} + 515q^{64} + 3852q^{65} - 2604q^{66} - 1061q^{67} - 32806q^{68} - 1278q^{69} - 2584q^{70} + 4000q^{71} - 306q^{72} + 7155q^{73} + 1288q^{74} - 999q^{75} - 2884q^{76} - 2246q^{77} + 792q^{78} + 2513q^{79} + 22708q^{80} - 1377q^{81} - 6136q^{82} + 2308q^{83} + 2718q^{84} - 6494q^{85} + 124q^{86} + 738q^{87} + 2782q^{88} + 1050q^{89} + 441q^{90} - 2750q^{91} + 1272q^{92} + 1422q^{93} + 2292q^{94} - 766q^{95} + 252q^{96} - 7450q^{97} + 3195q^{98} - 288q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
22.1 −5.28036 + 1.55045i −0.426945 2.96946i 18.7483 12.0488i 4.72579 10.3480i 6.85844 + 15.0179i −5.78549 + 1.69877i −51.4856 + 59.4175i −8.63544 + 2.53559i −8.90973 + 61.9685i
22.2 −4.44753 + 1.30591i −0.426945 2.96946i 11.3451 7.29106i −3.94539 + 8.63921i 5.77671 + 12.6492i 31.8454 9.35065i −16.6525 + 19.2180i −8.63544 + 2.53559i 6.26521 43.5755i
22.3 −4.13015 + 1.21272i −0.426945 2.96946i 8.85743 5.69232i 0.220201 0.482172i 5.36448 + 11.7466i −11.9166 + 3.49904i −7.12846 + 8.22668i −8.63544 + 2.53559i −0.324721 + 2.25849i
22.4 −3.63496 + 1.06732i −0.426945 2.96946i 5.34371 3.43419i −8.84178 + 19.3608i 4.72129 + 10.3382i −29.4141 + 8.63677i 4.08830 4.71815i −8.63544 + 2.53559i 11.4753 79.8127i
22.5 −2.34942 + 0.689852i −0.426945 2.96946i −1.68615 + 1.08362i 8.63833 18.9153i 3.05156 + 6.68199i 21.7576 6.38860i 16.0419 18.5133i −8.63544 + 2.53559i −7.24631 + 50.3992i
22.6 −2.05916 + 0.604624i −0.426945 2.96946i −2.85546 + 1.83509i 1.09436 2.39631i 2.67455 + 5.85646i −8.56947 + 2.51622i 16.0134 18.4805i −8.63544 + 2.53559i −0.804590 + 5.59605i
22.7 −1.71481 + 0.503514i −0.426945 2.96946i −4.04298 + 2.59827i −2.04662 + 4.48147i 2.22729 + 4.87710i 13.3024 3.90593i 14.9876 17.2967i −8.63544 + 2.53559i 1.25308 8.71537i
22.8 −0.550733 + 0.161710i −0.426945 2.96946i −6.45287 + 4.14701i 0.539245 1.18078i 0.715324 + 1.56634i −23.0466 + 6.76708i 5.89023 6.79769i −8.63544 + 2.53559i −0.106036 + 0.737496i
22.9 0.0808466 0.0237387i −0.426945 2.96946i −6.72406 + 4.32129i −8.02393 + 17.5699i −0.105008 0.229936i 6.29283 1.84774i −0.882462 + 1.01842i −8.63544 + 2.53559i −0.231619 + 1.61095i
22.10 1.06277 0.312057i −0.426945 2.96946i −5.69793 + 3.66184i 8.13725 17.8181i −1.38038 3.02262i −22.0932 + 6.48716i −10.7156 + 12.3665i −8.63544 + 2.53559i 3.08775 21.4758i
22.11 1.53570 0.450922i −0.426945 2.96946i −4.57498 + 2.94016i −1.67610 + 3.67015i −1.99466 4.36769i 22.8700 6.71525i −14.0850 + 16.2550i −8.63544 + 2.53559i −0.919036 + 6.39204i
22.12 1.62499 0.477141i −0.426945 2.96946i −4.31709 + 2.77442i 4.73615 10.3707i −2.11064 4.62165i 14.4183 4.23360i −14.5640 + 16.8078i −8.63544 + 2.53559i 2.74791 19.1122i
22.13 3.15128 0.925299i −0.426945 2.96946i 2.34435 1.50662i −1.02421 + 2.24270i −4.09306 8.96256i −27.5111 + 8.07799i −11.2125 + 12.9399i −8.63544 + 2.53559i −1.15239 + 8.01508i
22.14 3.31194 0.972475i −0.426945 2.96946i 3.29324 2.11644i −5.88287 + 12.8817i −4.30175 9.41951i −7.18856 + 2.11075i −9.23455 + 10.6572i −8.63544 + 2.53559i −6.95662 + 48.3844i
22.15 4.28771 1.25899i −0.426945 2.96946i 10.0694 6.47123i 4.82712 10.5699i −5.56913 12.1947i 18.6881 5.48732i 11.6165 13.4061i −8.63544 + 2.53559i 7.38992 51.3980i
22.16 4.88301 1.43378i −0.426945 2.96946i 15.0580 9.67718i −5.04604 + 11.0493i −6.34233 13.8878i 20.5808 6.04306i 32.9918 38.0746i −8.63544 + 2.53559i −8.79760 + 61.1887i
22.17 5.02605 1.47578i −0.426945 2.96946i 16.3532 10.5096i 5.16285 11.3051i −6.52812 14.2946i −25.0126 + 7.34437i 39.2397 45.2850i −8.63544 + 2.53559i 9.26494 64.4391i
25.1 −0.736275 5.12091i −1.96458 + 2.26725i −18.0056 + 5.28693i 8.38592 5.38931i 13.0568 + 8.39112i 3.11844 + 21.6892i 23.1376 + 50.6642i −1.28083 8.90839i −33.7725 38.9755i
25.2 −0.687211 4.77966i −1.96458 + 2.26725i −14.6969 + 4.31540i −18.1078 + 11.6372i 12.1867 + 7.83195i −0.920492 6.40216i 14.6783 + 32.1410i −1.28083 8.90839i 68.0655 + 78.5518i
25.3 −0.644593 4.48324i −1.96458 + 2.26725i −12.0080 + 3.52587i 1.80470 1.15981i 11.4310 + 7.34625i −3.01001 20.9351i 8.49516 + 18.6018i −1.28083 8.90839i −6.36302 7.34332i
See next 80 embeddings (of 170 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 196.17
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 \(T_{2}^{170} - \cdots\) acting on \(S_{4}^{\mathrm{new}}(201, [\chi])\).