Properties

Label 201.3.c.a
Level 201
Weight 3
Character orbit 201.c
Analytic conductor 5.477
Analytic rank 0
Dimension 44
CM No

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Newspace parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 201.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(44\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 44q - 92q^{4} + 6q^{6} + 8q^{7} + 4q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 44q - 92q^{4} + 6q^{6} + 8q^{7} + 4q^{9} + 12q^{10} - 20q^{12} - 32q^{13} - 30q^{15} + 204q^{16} + 22q^{18} - 32q^{19} + 36q^{21} - 8q^{22} - 24q^{24} - 164q^{25} + 42q^{27} - 48q^{28} + 58q^{30} + 20q^{31} + 6q^{33} - 48q^{34} - 78q^{36} + 100q^{37} + 4q^{39} + 160q^{40} - 204q^{42} - 108q^{43} - 132q^{45} - 244q^{46} + 34q^{48} + 332q^{49} + 114q^{51} - 8q^{52} + 432q^{54} + 128q^{55} - 26q^{57} - 12q^{58} + 250q^{60} - 164q^{61} - 290q^{63} - 432q^{64} - 78q^{66} + 76q^{69} + 612q^{70} - 464q^{72} + 156q^{73} - 118q^{75} - 180q^{76} - 392q^{79} + 348q^{81} + 524q^{82} - 202q^{84} - 188q^{85} - 68q^{87} - 348q^{88} + 94q^{90} - 44q^{91} + 322q^{93} - 304q^{94} + 224q^{96} + 68q^{97} + 104q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
68.1 3.85580i 2.40297 + 1.79604i −10.8672 6.40327i 6.92517 9.26536i 10.8148 26.4786i 2.54849 + 8.63164i 24.6898
68.2 3.83909i −0.0207392 2.99993i −10.7386 4.79169i −11.5170 + 0.0796199i 5.67115 25.8703i −8.99914 + 0.124433i −18.3957
68.3 3.74856i −2.69559 + 1.31674i −10.0517 4.74753i 4.93589 + 10.1046i −4.78098 22.6851i 5.53237 7.09880i −17.7964
68.4 3.48861i 2.56342 + 1.55849i −8.17041 4.65961i 5.43698 8.94276i −13.4680 14.5490i 4.14220 + 7.99013i −16.2556
68.5 3.36787i −2.80521 1.06340i −7.34253 7.21139i −3.58138 + 9.44756i −0.105037 11.2572i 6.73838 + 5.96610i 24.2870
68.6 3.10162i −1.15101 + 2.77041i −5.62003 1.67791i 8.59275 + 3.57000i 4.25449 5.02473i −6.35035 6.37755i 5.20424
68.7 2.87376i 2.67705 1.35402i −4.25852 2.14706i −3.89115 7.69322i 2.18513 0.742934i 5.33323 7.24959i 6.17014
68.8 2.85257i −0.383029 2.97545i −4.13715 2.94424i −8.48767 + 1.09262i −7.08182 0.391240i −8.70658 + 2.27937i 8.39866
68.9 2.83332i 2.79666 1.08567i −4.02771 6.23827i −3.07604 7.92385i 3.53484 0.0785029i 6.64266 6.07248i −17.6750
68.10 2.78110i −0.0951894 + 2.99849i −3.73454 3.67055i 8.33911 + 0.264732i −7.35767 0.738266i −8.98188 0.570849i 10.2082
68.11 2.37672i −2.91725 + 0.699765i −1.64880 3.76639i 1.66315 + 6.93348i 9.72750 5.58814i 8.02066 4.08278i −8.95165
68.12 2.26735i −2.13323 2.10934i −1.14089 6.81017i −4.78262 + 4.83679i −3.54429 6.48261i 0.101366 + 8.99943i −15.4411
68.13 1.84390i 1.97832 + 2.25527i 0.600017 2.65010i 4.15850 3.64784i 5.23167 8.48199i −1.17249 + 8.92330i −4.88653
68.14 1.81184i 0.454991 2.96530i 0.717236 6.02732i −5.37264 0.824371i 13.4974 8.54688i −8.58597 2.69837i 10.9205
68.15 1.74215i 2.96882 + 0.431379i 0.964903 9.03513i 0.751528 5.17214i −5.84306 8.64962i 8.62782 + 2.56137i 15.7406
68.16 1.16231i −2.84845 + 0.941451i 2.64903 5.51585i 1.09426 + 3.31079i −12.7350 7.72825i 7.22734 5.36336i 6.41115
68.17 1.01079i −0.770133 + 2.89946i 2.97831 8.93347i 2.93075 + 0.778442i −6.17840 7.05360i −7.81379 4.46595i −9.02986
68.18 0.898014i 1.52814 2.58162i 3.19357 1.98358i −2.31833 1.37229i −8.12242 6.45992i −4.32955 7.89018i −1.78129
68.19 0.846960i −2.75258 1.19301i 3.28266 3.42420i −1.01043 + 2.33133i 3.13578 6.16812i 6.15345 + 6.56773i 2.90016
68.20 0.777984i −1.77932 + 2.41537i 3.39474 2.01357i 1.87912 + 1.38428i 2.85306 5.75299i −2.66805 8.59543i 1.56652
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 68.44
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 \(S_{3}^{\mathrm{new}}(201, [\chi])\).