Properties

Label 560.2.x.b
Level 560
Weight 2
Character orbit 560.x
Analytic conductor 4.472
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.x (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24q + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q - 8q^{13} + 8q^{17} - 8q^{21} + 32q^{25} + 24q^{33} - 16q^{37} + 32q^{41} - 24q^{45} + 8q^{53} + 40q^{57} + 16q^{61} - 16q^{73} + 16q^{77} - 104q^{81} - 8q^{85} - 8q^{93} - 24q^{97} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
127.1 0 −2.31224 2.31224i 0 2.03291 + 0.931271i 0 0.707107 0.707107i 0 7.69286i 0
127.2 0 −1.77851 1.77851i 0 −2.23308 + 0.115477i 0 −0.707107 + 0.707107i 0 3.32619i 0
127.3 0 −1.38994 1.38994i 0 −0.674859 + 2.13180i 0 0.707107 0.707107i 0 0.863866i 0
127.4 0 −0.636375 0.636375i 0 1.68320 1.47202i 0 −0.707107 + 0.707107i 0 2.19005i 0
127.5 0 −0.333196 0.333196i 0 −2.17403 + 0.523047i 0 0.707107 0.707107i 0 2.77796i 0
127.6 0 −0.206273 0.206273i 0 1.36587 + 1.77043i 0 −0.707107 + 0.707107i 0 2.91490i 0
127.7 0 0.206273 + 0.206273i 0 1.36587 + 1.77043i 0 0.707107 0.707107i 0 2.91490i 0
127.8 0 0.333196 + 0.333196i 0 −2.17403 + 0.523047i 0 −0.707107 + 0.707107i 0 2.77796i 0
127.9 0 0.636375 + 0.636375i 0 1.68320 1.47202i 0 0.707107 0.707107i 0 2.19005i 0
127.10 0 1.38994 + 1.38994i 0 −0.674859 + 2.13180i 0 −0.707107 + 0.707107i 0 0.863866i 0
127.11 0 1.77851 + 1.77851i 0 −2.23308 + 0.115477i 0 0.707107 0.707107i 0 3.32619i 0
127.12 0 2.31224 + 2.31224i 0 2.03291 + 0.931271i 0 −0.707107 + 0.707107i 0 7.69286i 0
463.1 0 −2.31224 + 2.31224i 0 2.03291 0.931271i 0 0.707107 + 0.707107i 0 7.69286i 0
463.2 0 −1.77851 + 1.77851i 0 −2.23308 0.115477i 0 −0.707107 0.707107i 0 3.32619i 0
463.3 0 −1.38994 + 1.38994i 0 −0.674859 2.13180i 0 0.707107 + 0.707107i 0 0.863866i 0
463.4 0 −0.636375 + 0.636375i 0 1.68320 + 1.47202i 0 −0.707107 0.707107i 0 2.19005i 0
463.5 0 −0.333196 + 0.333196i 0 −2.17403 0.523047i 0 0.707107 + 0.707107i 0 2.77796i 0
463.6 0 −0.206273 + 0.206273i 0 1.36587 1.77043i 0 −0.707107 0.707107i 0 2.91490i 0
463.7 0 0.206273 0.206273i 0 1.36587 1.77043i 0 0.707107 + 0.707107i 0 2.91490i 0
463.8 0 0.333196 0.333196i 0 −2.17403 0.523047i 0 −0.707107 0.707107i 0 2.77796i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 463.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
5.c odd 4 1 inner
20.e even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 560.2.x.b 24
4.b odd 2 1 inner 560.2.x.b 24
5.c odd 4 1 inner 560.2.x.b 24
20.e even 4 1 inner 560.2.x.b 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
560.2.x.b 24 1.a even 1 1 trivial
560.2.x.b 24 4.b odd 2 1 inner
560.2.x.b 24 5.c odd 4 1 inner
560.2.x.b 24 20.e even 4 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{24} + 170 T_{3}^{20} + 7001 T_{3}^{16} + 73224 T_{3}^{12} + 48936 T_{3}^{8} + 2560 T_{3}^{4} + 16 \) acting on \(S_{2}^{\mathrm{new}}(560, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database