Properties

Label 287.3.v.a
Level 287
Weight 3
Character orbit 287.v
Analytic conductor 7.820
Analytic rank 0
Dimension 432
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 287.v (of order \(24\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(432\)
Relative dimension: \(54\) over \(\Q(\zeta_{24})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 432q - 4q^{2} - 4q^{3} - 4q^{5} - 16q^{6} - 8q^{7} - 48q^{8} - 36q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 432q - 4q^{2} - 4q^{3} - 4q^{5} - 16q^{6} - 8q^{7} - 48q^{8} - 36q^{9} - 8q^{10} - 4q^{11} - 76q^{12} - 16q^{13} - 100q^{14} - 40q^{15} + 760q^{16} - 40q^{17} - 8q^{18} + 44q^{19} - 448q^{20} - 160q^{21} - 32q^{22} + 228q^{24} + 60q^{26} - 16q^{27} - 72q^{28} - 112q^{29} + 244q^{30} - 128q^{32} - 192q^{33} - 16q^{34} - 32q^{35} + 272q^{36} + 64q^{37} + 24q^{38} - 4q^{39} - 16q^{41} - 336q^{42} - 224q^{43} - 228q^{44} - 396q^{46} + 156q^{47} - 1192q^{48} + 256q^{49} + 280q^{50} - 272q^{51} + 884q^{52} + 4q^{53} + 348q^{54} - 176q^{55} - 88q^{56} - 1168q^{57} - 280q^{58} - 8q^{59} - 524q^{60} + 220q^{61} - 48q^{62} + 412q^{63} + 160q^{65} + 444q^{67} + 172q^{68} - 472q^{69} - 132q^{70} + 288q^{71} + 32q^{73} + 280q^{74} - 528q^{75} + 600q^{76} - 232q^{77} - 912q^{78} - 216q^{79} - 904q^{80} - 52q^{82} + 704q^{83} + 1616q^{84} + 1216q^{85} + 520q^{87} + 456q^{88} + 36q^{89} + 1880q^{90} + 64q^{91} + 720q^{92} + 436q^{93} - 1456q^{94} + 220q^{95} - 1604q^{96} + 856q^{97} + 2376q^{98} - 752q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
44.1 −1.00113 3.73626i 4.33433 0.570626i −9.49326 + 5.48094i 6.12199 1.64038i −6.47122 15.6229i −6.59685 2.34128i 19.0416 + 19.0416i 9.76749 2.61719i −12.2578 21.2311i
44.2 −0.964481 3.59949i −2.15102 + 0.283187i −8.56202 + 4.94329i 4.97373 1.33271i 3.09394 + 7.46944i 6.47657 + 2.65595i 15.5112 + 15.5112i −4.14666 + 1.11109i −9.59414 16.6175i
44.3 −0.953963 3.56024i 3.93802 0.518450i −8.30116 + 4.79268i −6.13448 + 1.64373i −5.60253 13.5257i 2.91136 + 6.36584i 14.5570 + 14.5570i 6.54587 1.75396i 11.7041 + 20.2722i
44.4 −0.934785 3.48866i 0.164201 0.0216175i −7.83285 + 4.52230i −1.38302 + 0.370580i −0.228909 0.552635i 0.440489 6.98613i 12.8833 + 12.8833i −8.66684 + 2.32227i 2.58566 + 4.47849i
44.5 −0.895161 3.34079i −2.33888 + 0.307920i −6.89545 + 3.98109i −6.16719 + 1.65249i 3.12237 + 7.53807i −5.68361 + 4.08615i 9.69000 + 9.69000i −3.31778 + 0.888995i 11.0413 + 19.1240i
44.6 −0.845521 3.15553i −5.30986 + 0.699057i −5.77835 + 3.33613i −4.43760 + 1.18905i 6.69550 + 16.1644i 6.89536 + 1.20580i 6.17295 + 6.17295i 19.0126 5.09442i 7.50417 + 12.9976i
44.7 −0.822999 3.07147i −0.665898 + 0.0876672i −5.29251 + 3.05563i 6.18603 1.65754i 0.817301 + 1.97314i −2.80548 + 6.41321i 4.74713 + 4.74713i −8.25760 + 2.21262i −10.1822 17.6361i
44.8 −0.805923 3.00775i 2.67346 0.351967i −4.93293 + 2.84803i −4.41031 + 1.18174i −3.21323 7.75742i 6.30583 3.03916i 3.73441 + 3.73441i −1.66984 + 0.447433i 7.10875 + 12.3127i
44.9 −0.743556 2.77499i −4.02310 + 0.529651i −3.68360 + 2.12672i 5.12912 1.37434i 4.46118 + 10.7702i −1.22522 6.89194i 0.514865 + 0.514865i 7.21145 1.93230i −7.62758 13.2113i
44.10 −0.711148 2.65404i 4.57597 0.602438i −3.07410 + 1.77483i 5.06808 1.35799i −4.85309 11.7164i 5.42371 + 4.42530i −0.874947 0.874947i 11.8832 3.18410i −7.20831 12.4852i
44.11 −0.669740 2.49950i 1.94687 0.256310i −2.33487 + 1.34804i −2.15743 + 0.578081i −1.94454 4.69454i −6.88381 1.27009i −2.38587 2.38587i −4.96873 + 1.33137i 2.88983 + 5.00534i
44.12 −0.605293 2.25898i 5.84002 0.768853i −1.27252 + 0.734692i −4.08855 + 1.09552i −5.27175 12.7271i −1.90551 6.73565i −4.18485 4.18485i 24.8213 6.65085i 4.94953 + 8.57284i
44.13 −0.601567 2.24508i −4.60009 + 0.605614i −1.21439 + 0.701128i 1.97238 0.528497i 4.12691 + 9.96325i −6.51687 + 2.55546i −4.26942 4.26942i 12.1007 3.24239i −2.37303 4.11021i
44.14 −0.585405 2.18476i 2.68487 0.353470i −0.966375 + 0.557937i 7.59297 2.03453i −2.34399 5.65888i 2.78312 6.42295i −4.61274 4.61274i −1.60972 + 0.431323i −8.88992 15.3978i
44.15 −0.518206 1.93397i −0.899559 + 0.118429i −0.00760404 + 0.00439020i −3.55516 + 0.952603i 0.695196 + 1.67835i 5.90938 + 3.75223i −5.65063 5.65063i −7.89815 + 2.11630i 3.68461 + 6.38194i
44.16 −0.472662 1.76400i −3.59669 + 0.473513i 0.575817 0.332448i −8.51355 + 2.28120i 2.53530 + 6.12074i −2.12311 6.67026i −6.02395 6.02395i 4.01862 1.07679i 8.04807 + 13.9397i
44.17 −0.472042 1.76168i 0.937698 0.123450i 0.583396 0.336824i 2.21585 0.593735i −0.660113 1.59365i 2.05508 + 6.69153i −6.02733 6.02733i −7.82930 + 2.09785i −2.09195 3.62336i
44.18 −0.432281 1.61329i −1.08853 + 0.143308i 1.04825 0.605209i −2.34666 + 0.628787i 0.701750 + 1.69417i 5.57803 4.22914i −6.15357 6.15357i −7.52897 + 2.01738i 2.02884 + 3.51405i
44.19 −0.358555 1.33815i 2.81232 0.370250i 1.80203 1.04040i −9.33412 + 2.50107i −1.50382 3.63054i −3.19103 + 6.23036i −5.95670 5.95670i −0.921246 + 0.246847i 6.69359 + 11.5936i
44.20 −0.345775 1.29045i 0.635300 0.0836388i 1.91841 1.10759i 7.27076 1.94819i −0.327602 0.790901i −5.53537 4.28481i −5.87132 5.87132i −8.29672 + 2.22310i −5.02809 8.70890i
See next 80 embeddings (of 432 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 284.54
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner
41.e odd 8 1 inner
287.v odd 24 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 287.3.v.a 432
7.c even 3 1 inner 287.3.v.a 432
41.e odd 8 1 inner 287.3.v.a 432
287.v odd 24 1 inner 287.3.v.a 432
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
287.3.v.a 432 1.a even 1 1 trivial
287.3.v.a 432 7.c even 3 1 inner
287.3.v.a 432 41.e odd 8 1 inner
287.3.v.a 432 287.v odd 24 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(287, [\chi])\).