# Properties

 Label 187.2.h.a Level 187 Weight 2 Character orbit 187.h Analytic conductor 1.493 Analytic rank 0 Dimension 56 CM No

# Related objects

## Newspace parameters

 Level: $$N$$ = $$187 = 11 \cdot 17$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 187.h (of order $$8$$ and degree $$4$$)

## Newform invariants

 Self dual: No Analytic conductor: $$1.4932025178$$ Analytic rank: $$0$$ Dimension: $$56$$ Relative dimension: $$14$$ over $$\Q(\zeta_{8})$$ Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$56q - 16q^{6} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$56q - 16q^{6} - 16q^{10} - 16q^{14} + 24q^{15} - 32q^{16} + 8q^{17} - 24q^{19} + 16q^{20} - 24q^{24} - 8q^{25} - 48q^{27} - 40q^{32} + 16q^{33} + 64q^{34} + 32q^{35} + 64q^{36} + 8q^{37} - 32q^{39} + 96q^{40} - 24q^{41} - 8q^{42} - 32q^{43} + 16q^{44} - 32q^{45} - 16q^{46} - 24q^{48} - 112q^{50} - 48q^{51} + 8q^{53} - 72q^{54} + 64q^{56} + 40q^{57} + 16q^{58} + 16q^{59} - 8q^{60} - 64q^{61} + 56q^{62} + 16q^{63} + 56q^{65} + 24q^{67} - 88q^{68} - 64q^{69} - 96q^{70} - 16q^{71} + 8q^{73} - 48q^{74} + 40q^{75} + 88q^{76} + 136q^{78} - 32q^{80} + 104q^{82} - 56q^{83} + 80q^{84} - 8q^{85} - 32q^{86} + 56q^{87} - 32q^{91} + 40q^{92} + 8q^{93} + 16q^{94} + 48q^{95} + 64q^{96} - 16q^{97} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
100.1 −1.84901 1.84901i −0.451510 1.09004i 4.83767i 2.81371 1.16548i −1.18065 + 2.85034i 3.95652 + 1.63885i 5.24689 5.24689i 1.13699 1.13699i −7.35756 3.04760i
100.2 −1.45974 1.45974i −1.02130 2.46565i 2.26167i −1.65483 + 0.685451i −2.10836 + 5.09004i −0.400229 0.165780i 0.381975 0.381975i −2.91503 + 2.91503i 3.41619 + 1.41503i
100.3 −1.08694 1.08694i 1.18631 + 2.86400i 0.362879i 3.41797 1.41577i 1.82355 4.40244i 0.0878391 + 0.0363841i −1.77945 + 1.77945i −4.67384 + 4.67384i −5.25399 2.17627i
100.4 −1.05330 1.05330i 0.822167 + 1.98489i 0.218896i −2.95662 + 1.22467i 1.22470 2.95668i 2.38289 + 0.987023i −1.87604 + 1.87604i −1.14250 + 1.14250i 4.40417 + 1.82427i
100.5 −0.746627 0.746627i −0.160212 0.386786i 0.885097i 1.10648 0.458319i −0.169166 + 0.408404i −3.06195 1.26830i −2.15409 + 2.15409i 1.99738 1.99738i −1.16832 0.483934i
100.6 −0.394913 0.394913i −0.977881 2.36081i 1.68809i 2.76448 1.14508i −0.546138 + 1.31849i 0.872439 + 0.361376i −1.45647 + 1.45647i −2.49587 + 2.49587i −1.54394 0.639519i
100.7 −0.0934551 0.0934551i 0.130532 + 0.315131i 1.98253i −1.22394 + 0.506971i 0.0172518 0.0416495i 3.66916 + 1.51982i −0.372188 + 0.372188i 2.03905 2.03905i 0.161762 + 0.0670041i
100.8 0.131056 + 0.131056i 0.554134 + 1.33780i 1.96565i 1.85179 0.767036i −0.102704 + 0.247949i −0.551118 0.228280i 0.519723 0.519723i 0.638682 0.638682i 0.343213 + 0.142164i
100.9 0.258764 + 0.258764i −0.348316 0.840908i 1.86608i −3.82341 + 1.58371i 0.127465 0.307728i −3.92710 1.62666i 1.00040 1.00040i 1.53552 1.53552i −1.39917 0.579554i
100.10 0.834743 + 0.834743i 1.11249 + 2.68578i 0.606407i −1.44962 + 0.600451i −1.31330 + 3.17058i 0.348596 + 0.144393i 2.17568 2.17568i −3.85448 + 3.85448i −1.71128 0.708835i
100.11 1.05032 + 1.05032i −0.481365 1.16212i 0.206341i −0.514723 + 0.213205i 0.715008 1.72618i 2.93590 + 1.21609i 1.88391 1.88391i 1.00251 1.00251i −0.764557 0.316690i
100.12 1.12086 + 1.12086i −0.951848 2.29796i 0.512654i 0.910373 0.377089i 1.50881 3.64258i −2.04824 0.848409i 1.66711 1.66711i −2.25330 + 2.25330i 1.44307 + 0.597737i
100.13 1.46782 + 1.46782i 0.687197 + 1.65904i 2.30896i 1.34490 0.557076i −1.42649 + 3.44384i −4.08442 1.69182i −0.453500 + 0.453500i −0.158857 + 0.158857i 2.79175 + 1.15638i
100.14 1.82043 + 1.82043i −0.100390 0.242362i 4.62792i −1.17236 + 0.485606i 0.258451 0.623955i −0.180288 0.0746777i −4.78394 + 4.78394i 2.07266 2.07266i −3.01820 1.25018i
111.1 −1.71399 + 1.71399i 2.67857 + 1.10950i 3.87553i 0.851663 2.05610i −6.49271 + 2.68937i 0.471206 + 1.13759i 3.21463 + 3.21463i 3.82242 + 3.82242i 2.06439 + 4.98387i
111.2 −1.69733 + 1.69733i −1.82968 0.757880i 3.76185i 0.591807 1.42875i 4.39195 1.81920i 1.35574 + 3.27304i 2.99044 + 2.99044i 0.652042 + 0.652042i 1.42056 + 3.42955i
111.3 −1.63835 + 1.63835i 0.151924 + 0.0629292i 3.36837i 0.00973985 0.0235141i −0.352005 + 0.145805i −1.50462 3.63248i 2.24186 + 2.24186i −2.10220 2.10220i 0.0225670 + 0.0544815i
111.4 −1.31588 + 1.31588i −2.81689 1.16679i 1.46310i −1.53116 + 3.69655i 5.24206 2.17133i −1.11207 2.68478i −0.706501 0.706501i 4.45214 + 4.45214i −2.84940 6.87905i
111.5 −0.900361 + 0.900361i 0.234589 + 0.0971699i 0.378700i −0.780524 + 1.88435i −0.298703 + 0.123727i 0.838489 + 2.02429i −2.14169 2.14169i −2.07573 2.07573i −0.993844 2.39935i
111.6 −0.752683 + 0.752683i 2.22685 + 0.922393i 0.866938i −0.398376 + 0.961765i −2.37038 + 0.981845i 0.407287 + 0.983278i −2.15789 2.15789i 1.98675 + 1.98675i −0.424053 1.02375i
See all 56 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 155.14 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

This newform does not have CM; other inner twists have not been computed.

## Hecke kernels

There are no other newforms in $$S_{2}^{\mathrm{new}}(187, [\chi])$$.