# Properties

 Label 2736.2.cg.a Level $2736$ Weight $2$ Character orbit 2736.cg Analytic conductor $21.847$ Analytic rank $0$ Dimension $24$ CM no Inner twists $4$

# 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: $$24$$ Relative dimension: $$12$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$24q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q + 12q^{13} - 12q^{19} + 8q^{25} + 16q^{37} - 12q^{43} + 16q^{49} + 12q^{55} - 60q^{67} + 8q^{73} + 12q^{79} + 16q^{85} - 12q^{91} - 32q^{97} + O(q^{100})$$

## 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 −3.43403 1.98264i 0 2.01359i 0 0 0
1151.2 0 0 0 −2.27729 1.31480i 0 3.01718i 0 0 0
1151.3 0 0 0 −2.15944 1.24676i 0 0.872468i 0 0 0
1151.4 0 0 0 −1.62081 0.935772i 0 2.07786i 0 0 0
1151.5 0 0 0 −1.02690 0.592883i 0 4.00663i 0 0 0
1151.6 0 0 0 −0.420258 0.242636i 0 1.92619i 0 0 0
1151.7 0 0 0 0.420258 + 0.242636i 0 1.92619i 0 0 0
1151.8 0 0 0 1.02690 + 0.592883i 0 4.00663i 0 0 0
1151.9 0 0 0 1.62081 + 0.935772i 0 2.07786i 0 0 0
1151.10 0 0 0 2.15944 + 1.24676i 0 0.872468i 0 0 0
1151.11 0 0 0 2.27729 + 1.31480i 0 3.01718i 0 0 0
1151.12 0 0 0 3.43403 + 1.98264i 0 2.01359i 0 0 0
2591.1 0 0 0 −3.43403 + 1.98264i 0 2.01359i 0 0 0
2591.2 0 0 0 −2.27729 + 1.31480i 0 3.01718i 0 0 0
2591.3 0 0 0 −2.15944 + 1.24676i 0 0.872468i 0 0 0
2591.4 0 0 0 −1.62081 + 0.935772i 0 2.07786i 0 0 0
2591.5 0 0 0 −1.02690 + 0.592883i 0 4.00663i 0 0 0
2591.6 0 0 0 −0.420258 + 0.242636i 0 1.92619i 0 0 0
2591.7 0 0 0 0.420258 0.242636i 0 1.92619i 0 0 0
2591.8 0 0 0 1.02690 0.592883i 0 4.00663i 0 0 0
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 2591.12 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
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.a 24
3.b odd 2 1 inner 2736.2.cg.a 24
4.b odd 2 1 2736.2.cg.b yes 24
12.b even 2 1 2736.2.cg.b yes 24
19.c even 3 1 2736.2.cg.b yes 24
57.h odd 6 1 2736.2.cg.b yes 24
76.g odd 6 1 inner 2736.2.cg.a 24
228.m even 6 1 inner 2736.2.cg.a 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2736.2.cg.a 24 1.a even 1 1 trivial
2736.2.cg.a 24 3.b odd 2 1 inner
2736.2.cg.a 24 76.g odd 6 1 inner
2736.2.cg.a 24 228.m even 6 1 inner
2736.2.cg.b yes 24 4.b odd 2 1
2736.2.cg.b yes 24 12.b even 2 1
2736.2.cg.b yes 24 19.c even 3 1
2736.2.cg.b yes 24 57.h odd 6 1