# Properties

 Label 187.2.e.b Level 187 Weight 2 Character orbit 187.e Analytic conductor 1.493 Analytic rank 0 Dimension 28 CM No

# Related objects

## Newspace parameters

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

## Newform invariants

 Self dual: No Analytic conductor: $$1.4932025178$$ Analytic rank: $$0$$ Dimension: $$28$$ Relative dimension: $$14$$ over $$\Q(i)$$ Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$28q + 4q^{3} - 28q^{4} - 16q^{5} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$28q + 4q^{3} - 28q^{4} - 16q^{5} + 20q^{10} - 28q^{12} + 8q^{13} - 12q^{14} + 44q^{16} - 12q^{17} + 4q^{18} + 28q^{20} + 16q^{21} - 16q^{23} + 12q^{24} - 20q^{27} - 52q^{28} + 4q^{29} - 8q^{30} - 16q^{31} + 16q^{34} - 32q^{35} - 24q^{37} - 8q^{38} - 8q^{39} - 20q^{40} + 16q^{41} + 8q^{44} + 72q^{45} + 12q^{46} - 16q^{47} + 44q^{48} + 60q^{50} + 48q^{51} - 16q^{52} - 64q^{54} - 16q^{55} + 64q^{56} - 56q^{57} - 48q^{58} + 36q^{62} + 36q^{63} - 12q^{64} - 32q^{65} - 16q^{67} - 32q^{68} - 40q^{69} + 44q^{71} + 20q^{72} + 12q^{73} + 76q^{74} - 12q^{75} + 4q^{78} + 8q^{79} - 16q^{80} + 12q^{81} - 12q^{82} - 152q^{84} + 24q^{85} - 24q^{86} + 8q^{89} - 56q^{90} + 12q^{91} + 92q^{92} - 4q^{95} - 108q^{96} + 164q^{98} + 16q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
89.1 2.71846i 2.10133 2.10133i −5.39003 −0.643884 + 0.643884i −5.71237 5.71237i 1.95059 + 1.95059i 9.21565i 5.83115i 1.75037 + 1.75037i
89.2 2.53700i −0.691074 + 0.691074i −4.43636 −1.57614 + 1.57614i 1.75325 + 1.75325i −3.29211 3.29211i 6.18105i 2.04483i 3.99867 + 3.99867i
89.3 1.90463i −1.14033 + 1.14033i −1.62763 −2.29152 + 2.29152i 2.17192 + 2.17192i 3.32922 + 3.32922i 0.709222i 0.399285i 4.36451 + 4.36451i
89.4 1.23360i 1.72482 1.72482i 0.478229 −1.98987 + 1.98987i −2.12774 2.12774i −2.20951 2.20951i 3.05715i 2.94999i 2.45471 + 2.45471i
89.5 0.706093i −1.00523 + 1.00523i 1.50143 0.325349 0.325349i 0.709787 + 0.709787i 0.927032 + 0.927032i 2.47234i 0.979016i −0.229727 0.229727i
89.6 0.385060i 1.16534 1.16534i 1.85173 −0.671428 + 0.671428i −0.448724 0.448724i 1.38678 + 1.38678i 1.48315i 0.283977i 0.258540 + 0.258540i
89.7 0.0421125i −0.440583 + 0.440583i 1.99823 2.27271 2.27271i −0.0185541 0.0185541i −3.03167 3.03167i 0.168375i 2.61177i 0.0957096 + 0.0957096i
89.8 0.357045i −2.24825 + 2.24825i 1.87252 −2.10601 + 2.10601i −0.802728 0.802728i −1.27454 1.27454i 1.38266i 7.10929i −0.751939 0.751939i
89.9 1.19295i 1.79219 1.79219i 0.576868 0.279565 0.279565i 2.13799 + 2.13799i −2.05151 2.05151i 3.07408i 3.42386i 0.333507 + 0.333507i
89.10 1.26043i −0.0118422 + 0.0118422i 0.411321 −2.23893 + 2.23893i −0.0149262 0.0149262i −1.04178 1.04178i 3.03930i 2.99972i −2.82200 2.82200i
89.11 1.48649i −0.527154 + 0.527154i −0.209652 0.786278 0.786278i −0.783609 0.783609i 0.754002 + 0.754002i 2.66133i 2.44422i 1.16879 + 1.16879i
89.12 2.33488i 1.01883 1.01883i −3.45165 2.72560 2.72560i 2.37884 + 2.37884i 0.562655 + 0.562655i 3.38941i 0.923968i 6.36394 + 6.36394i
89.13 2.37074i −1.69274 + 1.69274i −3.62040 −0.324129 + 0.324129i −4.01304 4.01304i 1.08685 + 1.08685i 3.84154i 2.73072i −0.768424 0.768424i
89.14 2.44021i 1.95471 1.95471i −3.95461 −2.54760 + 2.54760i 4.76990 + 4.76990i 2.90400 + 2.90400i 4.76964i 4.64179i −6.21666 6.21666i
166.1 2.44021i 1.95471 + 1.95471i −3.95461 −2.54760 2.54760i 4.76990 4.76990i 2.90400 2.90400i 4.76964i 4.64179i −6.21666 + 6.21666i
166.2 2.37074i −1.69274 1.69274i −3.62040 −0.324129 0.324129i −4.01304 + 4.01304i 1.08685 1.08685i 3.84154i 2.73072i −0.768424 + 0.768424i
166.3 2.33488i 1.01883 + 1.01883i −3.45165 2.72560 + 2.72560i 2.37884 2.37884i 0.562655 0.562655i 3.38941i 0.923968i 6.36394 6.36394i
166.4 1.48649i −0.527154 0.527154i −0.209652 0.786278 + 0.786278i −0.783609 + 0.783609i 0.754002 0.754002i 2.66133i 2.44422i 1.16879 1.16879i
166.5 1.26043i −0.0118422 0.0118422i 0.411321 −2.23893 2.23893i −0.0149262 + 0.0149262i −1.04178 + 1.04178i 3.03930i 2.99972i −2.82200 + 2.82200i
166.6 1.19295i 1.79219 + 1.79219i 0.576868 0.279565 + 0.279565i 2.13799 2.13799i −2.05151 + 2.05151i 3.07408i 3.42386i 0.333507 0.333507i
See all 28 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 166.14 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

This newform can be constructed as the kernel of the linear operator $$T_{2}^{28} + \cdots$$ acting on $$S_{2}^{\mathrm{new}}(187, [\chi])$$.