# Properties

 Label 2736.2.d.b Level $2736$ Weight $2$ Character orbit 2736.d 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.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$21.8470699930$$ Analytic rank: $$0$$ Dimension: $$24$$ Twist minimal: yes 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.

 $$\operatorname{Tr}(f)(q) =$$ $$24q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q + 8q^{25} - 32q^{37} - 32q^{49} + 8q^{73} + 40q^{85} + 16q^{97} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
2015.1 0 0 0 2.95877i 0 0.569970i 0 0 0
2015.2 0 0 0 2.95877i 0 0.569970i 0 0 0
2015.3 0 0 0 2.62670i 0 0.815178i 0 0 0
2015.4 0 0 0 2.62670i 0 0.815178i 0 0 0
2015.5 0 0 0 2.30935i 0 4.59902i 0 0 0
2015.6 0 0 0 2.30935i 0 4.59902i 0 0 0
2015.7 0 0 0 2.03314i 0 3.00897i 0 0 0
2015.8 0 0 0 2.03314i 0 3.00897i 0 0 0
2015.9 0 0 0 1.28244i 0 4.16899i 0 0 0
2015.10 0 0 0 1.28244i 0 4.16899i 0 0 0
2015.11 0 0 0 1.11119i 0 1.19380i 0 0 0
2015.12 0 0 0 1.11119i 0 1.19380i 0 0 0
2015.13 0 0 0 1.11119i 0 1.19380i 0 0 0
2015.14 0 0 0 1.11119i 0 1.19380i 0 0 0
2015.15 0 0 0 1.28244i 0 4.16899i 0 0 0
2015.16 0 0 0 1.28244i 0 4.16899i 0 0 0
2015.17 0 0 0 2.03314i 0 3.00897i 0 0 0
2015.18 0 0 0 2.03314i 0 3.00897i 0 0 0
2015.19 0 0 0 2.30935i 0 4.59902i 0 0 0
2015.20 0 0 0 2.30935i 0 4.59902i 0 0 0
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 2015.24 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

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2736.2.d.b 24
3.b odd 2 1 inner 2736.2.d.b 24
4.b odd 2 1 inner 2736.2.d.b 24
12.b even 2 1 inner 2736.2.d.b 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2736.2.d.b 24 1.a even 1 1 trivial
2736.2.d.b 24 3.b odd 2 1 inner
2736.2.d.b 24 4.b odd 2 1 inner
2736.2.d.b 24 12.b even 2 1 inner

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{5}^{12} + 28 T_{5}^{10} + 305 T_{5}^{8} + 1632 T_{5}^{6} + 4440 T_{5}^{4} + 5696 T_{5}^{2} + 2704$$ acting on $$S_{2}^{\mathrm{new}}(2736, [\chi])$$.