# Properties

 Label 1155.2.i.d Level 1155 Weight 2 Character orbit 1155.i Analytic conductor 9.223 Analytic rank 0 Dimension 32 CM No

# Related objects

## Newspace parameters

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

## Newform invariants

 Self dual: No Analytic conductor: $$9.22272143346$$ Analytic rank: $$0$$ Dimension: $$32$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$32q$$ $$\mathstrut -\mathstrut 36q^{4}$$ $$\mathstrut -\mathstrut 32q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$32q$$ $$\mathstrut -\mathstrut 36q^{4}$$ $$\mathstrut -\mathstrut 32q^{9}$$ $$\mathstrut -\mathstrut 8q^{11}$$ $$\mathstrut -\mathstrut 28q^{14}$$ $$\mathstrut -\mathstrut 32q^{15}$$ $$\mathstrut +\mathstrut 44q^{16}$$ $$\mathstrut -\mathstrut 12q^{22}$$ $$\mathstrut +\mathstrut 4q^{23}$$ $$\mathstrut -\mathstrut 32q^{25}$$ $$\mathstrut +\mathstrut 36q^{36}$$ $$\mathstrut -\mathstrut 16q^{37}$$ $$\mathstrut +\mathstrut 8q^{42}$$ $$\mathstrut +\mathstrut 56q^{44}$$ $$\mathstrut +\mathstrut 16q^{49}$$ $$\mathstrut -\mathstrut 20q^{53}$$ $$\mathstrut +\mathstrut 52q^{56}$$ $$\mathstrut -\mathstrut 48q^{58}$$ $$\mathstrut +\mathstrut 36q^{60}$$ $$\mathstrut -\mathstrut 156q^{64}$$ $$\mathstrut -\mathstrut 72q^{67}$$ $$\mathstrut +\mathstrut 8q^{70}$$ $$\mathstrut +\mathstrut 48q^{71}$$ $$\mathstrut -\mathstrut 20q^{77}$$ $$\mathstrut -\mathstrut 8q^{78}$$ $$\mathstrut +\mathstrut 32q^{81}$$ $$\mathstrut +\mathstrut 56q^{86}$$ $$\mathstrut +\mathstrut 4q^{88}$$ $$\mathstrut -\mathstrut 80q^{91}$$ $$\mathstrut +\mathstrut 64q^{92}$$ $$\mathstrut +\mathstrut 32q^{93}$$ $$\mathstrut +\mathstrut 8q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
76.1 1.26491i 1.00000i 0.399993 1.00000i −1.26491 0.0556365 2.64517i 3.03578i −1.00000 −1.26491
76.2 1.26491i 1.00000i 0.399993 1.00000i −1.26491 0.0556365 + 2.64517i 3.03578i −1.00000 −1.26491
76.3 0.370647i 1.00000i 1.86262 1.00000i −0.370647 −2.39596 + 1.12222i 1.43167i −1.00000 −0.370647
76.4 0.370647i 1.00000i 1.86262 1.00000i −0.370647 −2.39596 1.12222i 1.43167i −1.00000 −0.370647
76.5 2.40558i 1.00000i −3.78682 1.00000i −2.40558 1.69010 2.03557i 4.29833i −1.00000 −2.40558
76.6 2.40558i 1.00000i −3.78682 1.00000i −2.40558 1.69010 + 2.03557i 4.29833i −1.00000 −2.40558
76.7 2.76869i 1.00000i −5.66565 1.00000i −2.76869 −2.02228 1.70599i 10.1491i −1.00000 −2.76869
76.8 2.76869i 1.00000i −5.66565 1.00000i −2.76869 −2.02228 + 1.70599i 10.1491i −1.00000 −2.76869
76.9 0.859876i 1.00000i 1.26061 1.00000i 0.859876 −2.42783 1.05149i 2.80372i −1.00000 0.859876
76.10 0.859876i 1.00000i 1.26061 1.00000i 0.859876 −2.42783 + 1.05149i 2.80372i −1.00000 0.859876
76.11 1.29033i 1.00000i 0.335051 1.00000i −1.29033 2.23077 + 1.42256i 3.01298i −1.00000 −1.29033
76.12 1.29033i 1.00000i 0.335051 1.00000i −1.29033 2.23077 1.42256i 3.01298i −1.00000 −1.29033
76.13 1.54704i 1.00000i −0.393347 1.00000i −1.54704 −2.51711 0.814965i 2.48556i −1.00000 −1.54704
76.14 1.54704i 1.00000i −0.393347 1.00000i −1.54704 −2.51711 + 0.814965i 2.48556i −1.00000 −1.54704
76.15 2.23885i 1.00000i −3.01246 1.00000i −2.23885 −0.322004 + 2.62608i 2.26674i −1.00000 −2.23885
76.16 2.23885i 1.00000i −3.01246 1.00000i −2.23885 −0.322004 2.62608i 2.26674i −1.00000 −2.23885
76.17 2.23885i 1.00000i −3.01246 1.00000i 2.23885 0.322004 + 2.62608i 2.26674i −1.00000 2.23885
76.18 2.23885i 1.00000i −3.01246 1.00000i 2.23885 0.322004 2.62608i 2.26674i −1.00000 2.23885
76.19 1.54704i 1.00000i −0.393347 1.00000i 1.54704 2.51711 0.814965i 2.48556i −1.00000 1.54704
76.20 1.54704i 1.00000i −0.393347 1.00000i 1.54704 2.51711 + 0.814965i 2.48556i −1.00000 1.54704
See all 32 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 76.32 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 $$T_{2}^{16} + \cdots$$ acting on $$S_{2}^{\mathrm{new}}(1155, [\chi])$$.