# Properties

 Label 2916.3.c.b Level 2916 Weight 3 Character orbit 2916.c Analytic conductor 79.455 Analytic rank 0 Dimension 36 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2916 = 2^{2} \cdot 3^{6}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 2916.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$79.4552450875$$ Analytic rank: $$0$$ Dimension: $$36$$ Twist minimal: no (minimal twist has level 108) 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.

 $$\operatorname{Tr}(f)(q) =$$ $$36q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$36q - 180q^{25} + 252q^{49} + 18q^{61} - 90q^{67} + 126q^{73} - 198q^{91} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1457.1 0 0 0 9.50324i 0 2.36132 0 0 0
1457.2 0 0 0 8.78835i 0 −4.31308 0 0 0
1457.3 0 0 0 7.78294i 0 3.61169 0 0 0
1457.4 0 0 0 7.77099i 0 13.6742 0 0 0
1457.5 0 0 0 7.31297i 0 −9.37121 0 0 0
1457.6 0 0 0 7.21405i 0 −4.39191 0 0 0
1457.7 0 0 0 5.21679i 0 −11.6618 0 0 0
1457.8 0 0 0 4.83775i 0 9.71048 0 0 0
1457.9 0 0 0 4.39539i 0 −3.57384 0 0 0
1457.10 0 0 0 4.19339i 0 −11.8514 0 0 0
1457.11 0 0 0 4.17955i 0 5.19980 0 0 0
1457.12 0 0 0 3.70301i 0 −0.419343 0 0 0
1457.13 0 0 0 3.34301i 0 5.01893 0 0 0
1457.14 0 0 0 2.96937i 0 0.934448 0 0 0
1457.15 0 0 0 2.16582i 0 6.23376 0 0 0
1457.16 0 0 0 1.52502i 0 −3.44709 0 0 0
1457.17 0 0 0 0.464464i 0 10.8001 0 0 0
1457.18 0 0 0 0.200781i 0 −8.51501 0 0 0
1457.19 0 0 0 0.200781i 0 −8.51501 0 0 0
1457.20 0 0 0 0.464464i 0 10.8001 0 0 0
See all 36 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1457.36 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2916.3.c.b 36
3.b odd 2 1 inner 2916.3.c.b 36
27.e even 9 1 108.3.k.a 36
27.e even 9 1 324.3.k.a 36
27.f odd 18 1 108.3.k.a 36
27.f odd 18 1 324.3.k.a 36
108.j odd 18 1 432.3.bc.b 36
108.l even 18 1 432.3.bc.b 36

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
108.3.k.a 36 27.e even 9 1
108.3.k.a 36 27.f odd 18 1
324.3.k.a 36 27.e even 9 1
324.3.k.a 36 27.f odd 18 1
432.3.bc.b 36 108.j odd 18 1
432.3.bc.b 36 108.l even 18 1
2916.3.c.b 36 1.a even 1 1 trivial
2916.3.c.b 36 3.b odd 2 1 inner

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database