# Properties

 Label 6048.2.h.i Level 6048 Weight 2 Character orbit 6048.h Analytic conductor 48.294 Analytic rank 0 Dimension 24 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.h (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$48.2935231425$$ Analytic rank: $$0$$ Dimension: $$24$$ Coefficient ring index: multiple of None 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.

 $$\operatorname{Tr}(f)(q) =$$ $$24q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q - 8q^{13} - 24q^{25} + 48q^{37} - 24q^{49} - 48q^{61} - 32q^{73} - 80q^{85} + 64q^{97} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
2591.1 0 0 0 4.29730i 0 1.00000i 0 0 0
2591.2 0 0 0 4.29730i 0 1.00000i 0 0 0
2591.3 0 0 0 0.865222i 0 1.00000i 0 0 0
2591.4 0 0 0 0.865222i 0 1.00000i 0 0 0
2591.5 0 0 0 2.64388i 0 1.00000i 0 0 0
2591.6 0 0 0 2.64388i 0 1.00000i 0 0 0
2591.7 0 0 0 2.76574i 0 1.00000i 0 0 0
2591.8 0 0 0 2.76574i 0 1.00000i 0 0 0
2591.9 0 0 0 1.29686i 0 1.00000i 0 0 0
2591.10 0 0 0 1.29686i 0 1.00000i 0 0 0
2591.11 0 0 0 0.680677i 0 1.00000i 0 0 0
2591.12 0 0 0 0.680677i 0 1.00000i 0 0 0
2591.13 0 0 0 0.680677i 0 1.00000i 0 0 0
2591.14 0 0 0 0.680677i 0 1.00000i 0 0 0
2591.15 0 0 0 1.29686i 0 1.00000i 0 0 0
2591.16 0 0 0 1.29686i 0 1.00000i 0 0 0
2591.17 0 0 0 2.76574i 0 1.00000i 0 0 0
2591.18 0 0 0 2.76574i 0 1.00000i 0 0 0
2591.19 0 0 0 2.64388i 0 1.00000i 0 0 0
2591.20 0 0 0 2.64388i 0 1.00000i 0 0 0
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 2591.24 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 6048.2.h.i 24
3.b odd 2 1 inner 6048.2.h.i 24
4.b odd 2 1 inner 6048.2.h.i 24
12.b even 2 1 inner 6048.2.h.i 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6048.2.h.i 24 1.a even 1 1 trivial
6048.2.h.i 24 3.b odd 2 1 inner
6048.2.h.i 24 4.b odd 2 1 inner
6048.2.h.i 24 12.b even 2 1 inner

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(6048, [\chi])$$:

 $$T_{5}^{12} + 36 T_{5}^{10} + 422 T_{5}^{8} + 2004 T_{5}^{6} + 3649 T_{5}^{4} + 2544 T_{5}^{2} + 576$$ $$T_{11}^{12} - 88 T_{11}^{10} + 2856 T_{11}^{8} - 42880 T_{11}^{6} + 307984 T_{11}^{4} - 1016448 T_{11}^{2} + 1218816$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database