Properties

Label 187.2.m.a
Level 187
Weight 2
Character orbit 187.m
Analytic conductor 1.493
Analytic rank 0
Dimension 128
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 187 = 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 187.m (of order \(16\) and degree \(8\))

Newform invariants

Self dual: No
Analytic conductor: \(1.4932025178\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(16\) over \(\Q(\zeta_{16})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 128q - 16q^{3} - 16q^{4} - 16q^{5} - 16q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 128q - 16q^{3} - 16q^{4} - 16q^{5} - 16q^{9} - 64q^{12} + 16q^{14} - 16q^{15} - 16q^{20} + 8q^{22} - 32q^{23} + 16q^{26} + 32q^{27} - 80q^{31} - 16q^{34} + 16q^{36} + 16q^{37} + 80q^{38} - 112q^{42} - 72q^{44} - 16q^{45} - 16q^{47} + 32q^{48} + 48q^{49} - 16q^{53} - 8q^{55} - 16q^{56} - 128q^{58} + 48q^{59} + 112q^{60} + 48q^{64} + 72q^{66} - 192q^{69} + 128q^{70} - 16q^{71} + 48q^{75} + 8q^{77} - 16q^{78} + 112q^{80} - 16q^{82} + 32q^{86} - 168q^{88} - 16q^{89} + 144q^{91} - 176q^{92} + 48q^{93} + 48q^{97} - 112q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
10.1 −2.31737 0.959888i 0.0998402 + 0.0667111i 3.03462 + 3.03462i −1.55498 + 0.309305i −0.167332 0.250430i −0.0889145 + 0.447003i −2.19968 5.31050i −1.14253 2.75832i 3.90037 + 0.775832i
10.2 −2.25162 0.932652i −2.66909 1.78343i 2.78574 + 2.78574i 2.54233 0.505701i 4.34645 + 6.50493i −0.607350 + 3.05336i −1.80901 4.36732i 2.79536 + 6.74860i −6.19601 1.23246i
10.3 −1.58527 0.656642i 2.26689 + 1.51468i 0.667703 + 0.667703i −3.74296 + 0.744522i −2.59903 3.88972i −0.334093 + 1.67960i 0.693234 + 1.67362i 1.69645 + 4.09559i 6.42251 + 1.27752i
10.4 −1.50318 0.622639i 1.02275 + 0.683380i 0.457668 + 0.457668i 0.908813 0.180774i −1.11188 1.66405i 0.274197 1.37848i 0.842281 + 2.03345i −0.569040 1.37378i −1.47867 0.294126i
10.5 −1.30126 0.539000i −2.38581 1.59415i −0.0114548 0.0114548i −3.07041 + 0.610742i 2.24531 + 3.36035i 0.785949 3.95123i 1.08673 + 2.62360i 2.00273 + 4.83502i 4.32459 + 0.860214i
10.6 −0.896657 0.371407i −1.08522 0.725122i −0.748164 0.748164i 2.89314 0.575481i 0.703755 + 1.05324i 0.0961645 0.483452i 1.13579 + 2.74203i −0.496147 1.19780i −2.80789 0.558524i
10.7 −0.821699 0.340359i −1.10085 0.735567i −0.854868 0.854868i −1.20971 + 0.240627i 0.654214 + 0.979100i −0.644166 + 3.23844i 1.09220 + 2.63681i −0.477230 1.15214i 1.07592 + 0.214014i
10.8 −0.198710 0.0823085i 2.14439 + 1.43283i −1.38150 1.38150i 1.69258 0.336675i −0.308177 0.461220i 0.860605 4.32655i 0.325427 + 0.785649i 1.39733 + 3.37345i −0.364045 0.0724130i
10.9 0.198710 + 0.0823085i 2.14439 + 1.43283i −1.38150 1.38150i 1.69258 0.336675i 0.308177 + 0.461220i −0.860605 + 4.32655i −0.325427 0.785649i 1.39733 + 3.37345i 0.364045 + 0.0724130i
10.10 0.821699 + 0.340359i −1.10085 0.735567i −0.854868 0.854868i −1.20971 + 0.240627i −0.654214 0.979100i 0.644166 3.23844i −1.09220 2.63681i −0.477230 1.15214i −1.07592 0.214014i
10.11 0.896657 + 0.371407i −1.08522 0.725122i −0.748164 0.748164i 2.89314 0.575481i −0.703755 1.05324i −0.0961645 + 0.483452i −1.13579 2.74203i −0.496147 1.19780i 2.80789 + 0.558524i
10.12 1.30126 + 0.539000i −2.38581 1.59415i −0.0114548 0.0114548i −3.07041 + 0.610742i −2.24531 3.36035i −0.785949 + 3.95123i −1.08673 2.62360i 2.00273 + 4.83502i −4.32459 0.860214i
10.13 1.50318 + 0.622639i 1.02275 + 0.683380i 0.457668 + 0.457668i 0.908813 0.180774i 1.11188 + 1.66405i −0.274197 + 1.37848i −0.842281 2.03345i −0.569040 1.37378i 1.47867 + 0.294126i
10.14 1.58527 + 0.656642i 2.26689 + 1.51468i 0.667703 + 0.667703i −3.74296 + 0.744522i 2.59903 + 3.88972i 0.334093 1.67960i −0.693234 1.67362i 1.69645 + 4.09559i −6.42251 1.27752i
10.15 2.25162 + 0.932652i −2.66909 1.78343i 2.78574 + 2.78574i 2.54233 0.505701i −4.34645 6.50493i 0.607350 3.05336i 1.80901 + 4.36732i 2.79536 + 6.74860i 6.19601 + 1.23246i
10.16 2.31737 + 0.959888i 0.0998402 + 0.0667111i 3.03462 + 3.03462i −1.55498 + 0.309305i 0.167332 + 0.250430i 0.0889145 0.447003i 2.19968 + 5.31050i −1.14253 2.75832i −3.90037 0.775832i
54.1 −1.05312 2.54247i 1.00237 + 0.199384i −3.94085 + 3.94085i −0.856163 1.28134i −0.548692 2.75846i −2.87065 1.91811i 9.08474 + 3.76302i −1.80665 0.748339i −2.35611 + 3.52617i
54.2 −0.926579 2.23696i −1.59986 0.318232i −2.73122 + 2.73122i 1.86996 + 2.79859i 0.770525 + 3.87369i 2.28141 + 1.52439i 4.16641 + 1.72579i −0.313354 0.129795i 4.52767 6.77614i
54.3 −0.791873 1.91175i 2.13852 + 0.425377i −1.61351 + 1.61351i 0.428580 + 0.641415i −0.880218 4.42515i 3.78229 + 2.52725i 0.538832 + 0.223192i 1.62067 + 0.671303i 0.886844 1.32726i
54.4 −0.657401 1.58711i −0.508365 0.101120i −0.672515 + 0.672515i 0.528726 + 0.791294i 0.173711 + 0.873306i −3.14310 2.10015i −1.66475 0.689561i −2.52343 1.04524i 0.908282 1.35934i
See next 80 embeddings (of 128 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 175.16
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 \(S_{2}^{\mathrm{new}}(187, [\chi])\).