# Properties

 Label 2736.2.cg.c Level $2736$ Weight $2$ Character orbit 2736.cg Analytic conductor $21.847$ Analytic rank $0$ Dimension $32$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2736.cg (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$21.8470699930$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(\zeta_{6})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$32q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$32q - 16q^{13} + 24q^{25} - 16q^{37} - 96q^{49} - 8q^{61} - 8q^{73} + 16q^{85} + 48q^{97} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1151.1 0 0 0 −3.37787 1.95021i 0 3.27561i 0 0 0
1151.2 0 0 0 −3.37787 1.95021i 0 3.27561i 0 0 0
1151.3 0 0 0 −2.03864 1.17701i 0 4.52875i 0 0 0
1151.4 0 0 0 −2.03864 1.17701i 0 4.52875i 0 0 0
1151.5 0 0 0 −1.45856 0.842100i 0 0.172239i 0 0 0
1151.6 0 0 0 −1.45856 0.842100i 0 0.172239i 0 0 0
1151.7 0 0 0 −1.34408 0.776006i 0 2.95486i 0 0 0
1151.8 0 0 0 −1.34408 0.776006i 0 2.95486i 0 0 0
1151.9 0 0 0 1.34408 + 0.776006i 0 2.95486i 0 0 0
1151.10 0 0 0 1.34408 + 0.776006i 0 2.95486i 0 0 0
1151.11 0 0 0 1.45856 + 0.842100i 0 0.172239i 0 0 0
1151.12 0 0 0 1.45856 + 0.842100i 0 0.172239i 0 0 0
1151.13 0 0 0 2.03864 + 1.17701i 0 4.52875i 0 0 0
1151.14 0 0 0 2.03864 + 1.17701i 0 4.52875i 0 0 0
1151.15 0 0 0 3.37787 + 1.95021i 0 3.27561i 0 0 0
1151.16 0 0 0 3.37787 + 1.95021i 0 3.27561i 0 0 0
2591.1 0 0 0 −3.37787 + 1.95021i 0 3.27561i 0 0 0
2591.2 0 0 0 −3.37787 + 1.95021i 0 3.27561i 0 0 0
2591.3 0 0 0 −2.03864 + 1.17701i 0 4.52875i 0 0 0
2591.4 0 0 0 −2.03864 + 1.17701i 0 4.52875i 0 0 0
See all 32 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 2591.16 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
4.b odd 2 1 inner
12.b even 2 1 inner
19.c even 3 1 inner
57.h odd 6 1 inner
76.g odd 6 1 inner
228.m even 6 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2736.2.cg.c 32
3.b odd 2 1 inner 2736.2.cg.c 32
4.b odd 2 1 inner 2736.2.cg.c 32
12.b even 2 1 inner 2736.2.cg.c 32
19.c even 3 1 inner 2736.2.cg.c 32
57.h odd 6 1 inner 2736.2.cg.c 32
76.g odd 6 1 inner 2736.2.cg.c 32
228.m even 6 1 inner 2736.2.cg.c 32

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2736.2.cg.c 32 1.a even 1 1 trivial
2736.2.cg.c 32 3.b odd 2 1 inner
2736.2.cg.c 32 4.b odd 2 1 inner
2736.2.cg.c 32 12.b even 2 1 inner
2736.2.cg.c 32 19.c even 3 1 inner
2736.2.cg.c 32 57.h odd 6 1 inner
2736.2.cg.c 32 76.g odd 6 1 inner
2736.2.cg.c 32 228.m even 6 1 inner