# Properties

 Label 6048.2.j.d Level 6048 Weight 2 Character orbit 6048.j Analytic conductor 48.294 Analytic rank 0 Dimension 48 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ = $$6048 = 2^{5} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 6048.j (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$48.2935231425$$ Analytic rank: $$0$$ Dimension: $$48$$ Coefficient ring index: multiple of None Twist minimal: no (minimal twist has level 1512) 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.

 $$\operatorname{Tr}(f)(q) =$$ $$48q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$48q - 16q^{19} + 48q^{25} - 64q^{43} - 48q^{49} - 32q^{67} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
5615.1 0 0 0 −4.18263 0 1.00000i 0 0 0
5615.2 0 0 0 −4.18263 0 1.00000i 0 0 0
5615.3 0 0 0 −3.69622 0 1.00000i 0 0 0
5615.4 0 0 0 −3.69622 0 1.00000i 0 0 0
5615.5 0 0 0 −2.99711 0 1.00000i 0 0 0
5615.6 0 0 0 −2.99711 0 1.00000i 0 0 0
5615.7 0 0 0 −2.90802 0 1.00000i 0 0 0
5615.8 0 0 0 −2.90802 0 1.00000i 0 0 0
5615.9 0 0 0 −2.85878 0 1.00000i 0 0 0
5615.10 0 0 0 −2.85878 0 1.00000i 0 0 0
5615.11 0 0 0 −2.35025 0 1.00000i 0 0 0
5615.12 0 0 0 −2.35025 0 1.00000i 0 0 0
5615.13 0 0 0 −2.29653 0 1.00000i 0 0 0
5615.14 0 0 0 −2.29653 0 1.00000i 0 0 0
5615.15 0 0 0 −1.27819 0 1.00000i 0 0 0
5615.16 0 0 0 −1.27819 0 1.00000i 0 0 0
5615.17 0 0 0 −1.27600 0 1.00000i 0 0 0
5615.18 0 0 0 −1.27600 0 1.00000i 0 0 0
5615.19 0 0 0 −0.863507 0 1.00000i 0 0 0
5615.20 0 0 0 −0.863507 0 1.00000i 0 0 0
See all 48 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 5615.48 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
8.d odd 2 1 inner
24.f even 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6048.2.j.d 48
3.b odd 2 1 inner 6048.2.j.d 48
4.b odd 2 1 1512.2.j.d 48
8.b even 2 1 1512.2.j.d 48
8.d odd 2 1 inner 6048.2.j.d 48
12.b even 2 1 1512.2.j.d 48
24.f even 2 1 inner 6048.2.j.d 48
24.h odd 2 1 1512.2.j.d 48

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1512.2.j.d 48 4.b odd 2 1
1512.2.j.d 48 8.b even 2 1
1512.2.j.d 48 12.b even 2 1
1512.2.j.d 48 24.h odd 2 1
6048.2.j.d 48 1.a even 1 1 trivial
6048.2.j.d 48 3.b odd 2 1 inner
6048.2.j.d 48 8.d odd 2 1 inner
6048.2.j.d 48 24.f even 2 1 inner

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{5}^{24} - \cdots$$ acting on $$S_{2}^{\mathrm{new}}(6048, [\chi])$$.

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database