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 $4$

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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:

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 \(S_{2}^{\mathrm{new}}(2736, [\chi])\).