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

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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:

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