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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 $2$

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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.

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

Display 100 coefficients 10 coefficients

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:

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 \(S_{2}^{\mathrm{new}}(5520, [\chi])\).