# Properties

 Label 1155.3.b.a Level 1155 Weight 3 Character orbit 1155.b Analytic conductor 31.471 Analytic rank 0 Dimension 96 CM No

# Related objects

## Newspace parameters

 Level: $$N$$ = $$1155 = 3 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$3$$ Character orbit: $$[\chi]$$ = 1155.b (of order $$2$$ and degree $$1$$)

## Newform invariants

 Self dual: No Analytic conductor: $$31.4714705336$$ Analytic rank: $$0$$ Dimension: $$96$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$96q$$ $$\mathstrut -\mathstrut 216q^{4}$$ $$\mathstrut +\mathstrut 288q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$96q$$ $$\mathstrut -\mathstrut 216q^{4}$$ $$\mathstrut +\mathstrut 288q^{9}$$ $$\mathstrut +\mathstrut 40q^{11}$$ $$\mathstrut -\mathstrut 56q^{14}$$ $$\mathstrut +\mathstrut 488q^{16}$$ $$\mathstrut +\mathstrut 56q^{22}$$ $$\mathstrut +\mathstrut 16q^{23}$$ $$\mathstrut +\mathstrut 480q^{25}$$ $$\mathstrut -\mathstrut 64q^{26}$$ $$\mathstrut +\mathstrut 192q^{31}$$ $$\mathstrut +\mathstrut 24q^{33}$$ $$\mathstrut +\mathstrut 176q^{34}$$ $$\mathstrut -\mathstrut 648q^{36}$$ $$\mathstrut -\mathstrut 112q^{37}$$ $$\mathstrut -\mathstrut 272q^{38}$$ $$\mathstrut -\mathstrut 520q^{44}$$ $$\mathstrut +\mathstrut 416q^{47}$$ $$\mathstrut -\mathstrut 192q^{48}$$ $$\mathstrut -\mathstrut 672q^{49}$$ $$\mathstrut +\mathstrut 112q^{53}$$ $$\mathstrut -\mathstrut 80q^{55}$$ $$\mathstrut +\mathstrut 280q^{56}$$ $$\mathstrut -\mathstrut 352q^{58}$$ $$\mathstrut +\mathstrut 512q^{59}$$ $$\mathstrut -\mathstrut 1112q^{64}$$ $$\mathstrut +\mathstrut 288q^{66}$$ $$\mathstrut -\mathstrut 304q^{67}$$ $$\mathstrut -\mathstrut 480q^{71}$$ $$\mathstrut +\mathstrut 224q^{77}$$ $$\mathstrut +\mathstrut 240q^{78}$$ $$\mathstrut +\mathstrut 864q^{81}$$ $$\mathstrut -\mathstrut 720q^{82}$$ $$\mathstrut -\mathstrut 432q^{86}$$ $$\mathstrut -\mathstrut 376q^{88}$$ $$\mathstrut -\mathstrut 32q^{89}$$ $$\mathstrut -\mathstrut 384q^{92}$$ $$\mathstrut +\mathstrut 384q^{93}$$ $$\mathstrut +\mathstrut 272q^{97}$$ $$\mathstrut +\mathstrut 120q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
736.1 3.97461i −1.73205 −11.7975 −2.23607 6.88422i 2.64575i 30.9920i 3.00000 8.88749i
736.2 3.80731i −1.73205 −10.4956 −2.23607 6.59446i 2.64575i 24.7309i 3.00000 8.51341i
736.3 3.79404i 1.73205 −10.3948 2.23607 6.57148i 2.64575i 24.2621i 3.00000 8.48374i
736.4 3.73924i 1.73205 −9.98188 −2.23607 6.47655i 2.64575i 22.3677i 3.00000 8.36118i
736.5 3.73084i −1.73205 −9.91918 2.23607 6.46201i 2.64575i 22.0835i 3.00000 8.34242i
736.6 3.67613i 1.73205 −9.51395 −2.23607 6.36725i 2.64575i 20.2700i 3.00000 8.22008i
736.7 3.66479i −1.73205 −9.43072 2.23607 6.34761i 2.64575i 19.9025i 3.00000 8.19473i
736.8 3.64908i 1.73205 −9.31580 2.23607 6.32039i 2.64575i 19.3978i 3.00000 8.15959i
736.9 3.57619i −1.73205 −8.78910 2.23607 6.19413i 2.64575i 17.1267i 3.00000 7.99659i
736.10 3.57202i 1.73205 −8.75932 −2.23607 6.18692i 2.64575i 17.0004i 3.00000 7.98728i
736.11 3.29262i 1.73205 −6.84133 2.23607 5.70298i 2.64575i 9.35542i 3.00000 7.36252i
736.12 3.27785i −1.73205 −6.74433 −2.23607 5.67741i 2.64575i 8.99550i 3.00000 7.32950i
736.13 3.25995i 1.73205 −6.62729 2.23607 5.64640i 2.64575i 8.56486i 3.00000 7.28948i
736.14 2.97479i 1.73205 −4.84935 2.23607 5.15248i 2.64575i 2.52665i 3.00000 6.65182i
736.15 2.94196i 1.73205 −4.65512 −2.23607 5.09562i 2.64575i 1.92733i 3.00000 6.57842i
736.16 2.91962i −1.73205 −4.52416 2.23607 5.05692i 2.64575i 1.53034i 3.00000 6.52846i
736.17 2.91387i −1.73205 −4.49063 2.23607 5.04697i 2.64575i 1.42964i 3.00000 6.51561i
736.18 2.89693i −1.73205 −4.39221 2.23607 5.01763i 2.64575i 1.13621i 3.00000 6.47774i
736.19 2.81721i −1.73205 −3.93666 −2.23607 4.87955i 2.64575i 0.178435i 3.00000 6.29947i
736.20 2.77171i −1.73205 −3.68240 −2.23607 4.80075i 2.64575i 0.880291i 3.00000 6.19774i
See all 96 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 736.96 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 $$S_{3}^{\mathrm{new}}(1155, [\chi])$$.