# Properties

 Label 5520.2.be.c Level $5520$ Weight $2$ Character orbit 5520.be Analytic conductor $44.077$ Analytic rank $0$ Dimension $32$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5520.be (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$44.0774219157$$ Analytic rank: $$0$$ Dimension: $$32$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$32q - 8q^{7} - 32q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$32q - 8q^{7} - 32q^{9} + 8q^{11} - 8q^{13} - 32q^{15} - 32q^{25} + 4q^{29} + 20q^{41} + 52q^{49} - 4q^{51} + 8q^{63} + 32q^{67} - 40q^{73} - 24q^{77} + 32q^{79} + 32q^{81} - 4q^{85} - 48q^{91} - 8q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1471.1 0 1.00000i 0 1.00000i 0 3.34851 0 −1.00000 0
1471.2 0 1.00000i 0 1.00000i 0 3.34851 0 −1.00000 0
1471.3 0 1.00000i 0 1.00000i 0 −1.52302 0 −1.00000 0
1471.4 0 1.00000i 0 1.00000i 0 −1.52302 0 −1.00000 0
1471.5 0 1.00000i 0 1.00000i 0 3.12483 0 −1.00000 0
1471.6 0 1.00000i 0 1.00000i 0 3.12483 0 −1.00000 0
1471.7 0 1.00000i 0 1.00000i 0 3.67125 0 −1.00000 0
1471.8 0 1.00000i 0 1.00000i 0 3.67125 0 −1.00000 0
1471.9 0 1.00000i 0 1.00000i 0 −1.53388 0 −1.00000 0
1471.10 0 1.00000i 0 1.00000i 0 −1.53388 0 −1.00000 0
1471.11 0 1.00000i 0 1.00000i 0 −2.13359 0 −1.00000 0
1471.12 0 1.00000i 0 1.00000i 0 −2.13359 0 −1.00000 0
1471.13 0 1.00000i 0 1.00000i 0 −3.74981 0 −1.00000 0
1471.14 0 1.00000i 0 1.00000i 0 −3.74981 0 −1.00000 0
1471.15 0 1.00000i 0 1.00000i 0 3.60511 0 −1.00000 0
1471.16 0 1.00000i 0 1.00000i 0 3.60511 0 −1.00000 0
1471.17 0 1.00000i 0 1.00000i 0 −0.143131 0 −1.00000 0
1471.18 0 1.00000i 0 1.00000i 0 −0.143131 0 −1.00000 0
1471.19 0 1.00000i 0 1.00000i 0 −2.01693 0 −1.00000 0
1471.20 0 1.00000i 0 1.00000i 0 −2.01693 0 −1.00000 0
See all 32 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1471.32 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

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

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5520.2.be.c 32
4.b odd 2 1 5520.2.be.d yes 32
23.b odd 2 1 5520.2.be.d yes 32
92.b even 2 1 inner 5520.2.be.c 32

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5520.2.be.c 32 1.a even 1 1 trivial
5520.2.be.c 32 92.b even 2 1 inner
5520.2.be.d yes 32 4.b odd 2 1
5520.2.be.d yes 32 23.b odd 2 1

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{7}^{16} + \cdots$$ acting on $$S_{2}^{\mathrm{new}}(5520, [\chi])$$.