Properties

Label 552.2.u.a
Level $552$
Weight $2$
Character orbit 552.u
Analytic conductor $4.408$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.u (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(24\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 240q - 4q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 240q - 4q^{9} - 16q^{25} + 12q^{27} - 8q^{31} + 44q^{37} + 20q^{39} + 44q^{43} + 124q^{49} + 12q^{55} + 16q^{69} - 74q^{75} - 144q^{81} + 24q^{85} - 170q^{87} + 12q^{93} - 198q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 0 −1.68738 0.390832i 0 3.08209 1.98074i 0 0.266085 + 0.0382572i 0 2.69450 + 1.31896i 0
17.2 0 −1.63887 + 0.560462i 0 0.535830 0.344357i 0 −2.02223 0.290753i 0 2.37176 1.83704i 0
17.3 0 −1.63081 0.583477i 0 −3.08209 + 1.98074i 0 0.266085 + 0.0382572i 0 2.31911 + 1.90309i 0
17.4 0 −1.52304 + 0.824833i 0 −1.21140 + 0.778520i 0 4.71345 + 0.677692i 0 1.63930 2.51251i 0
17.5 0 −1.49329 + 0.877542i 0 −2.99625 + 1.92558i 0 −3.72244 0.535207i 0 1.45984 2.62085i 0
17.6 0 −1.21330 + 1.23609i 0 1.30091 0.836045i 0 2.87937 + 0.413991i 0 −0.0558237 2.99948i 0
17.7 0 −1.07569 1.35753i 0 −0.535830 + 0.344357i 0 −2.02223 0.290753i 0 −0.685767 + 2.92057i 0
17.8 0 −0.835324 1.51731i 0 1.21140 0.778520i 0 4.71345 + 0.677692i 0 −1.60447 + 2.53489i 0
17.9 0 −0.781802 1.54557i 0 2.99625 1.92558i 0 −3.72244 0.535207i 0 −1.77757 + 2.41666i 0
17.10 0 −0.725957 + 1.57257i 0 1.91532 1.23090i 0 −2.52083 0.362441i 0 −1.94597 2.28324i 0
17.11 0 −0.352411 1.69582i 0 −1.30091 + 0.836045i 0 2.87937 + 0.413991i 0 −2.75161 + 1.19525i 0
17.12 0 0.0283990 + 1.73182i 0 −2.72873 + 1.75365i 0 3.60100 + 0.517745i 0 −2.99839 + 0.0983638i 0
17.13 0 0.0794015 + 1.73023i 0 −0.260753 + 0.167576i 0 0.155773 + 0.0223967i 0 −2.98739 + 0.274766i 0
17.14 0 0.239483 1.71541i 0 −1.91532 + 1.23090i 0 −2.52083 0.362441i 0 −2.88530 0.821626i 0
17.15 0 0.441043 + 1.67496i 0 3.16079 2.03132i 0 −2.34525 0.337196i 0 −2.61096 + 1.47746i 0
17.16 0 0.908372 + 1.47474i 0 −1.46204 + 0.939594i 0 −4.39604 0.632056i 0 −1.34972 + 2.67923i 0
17.17 0 0.960182 1.44154i 0 2.72873 1.75365i 0 3.60100 + 0.517745i 0 −1.15610 2.76829i 0
17.18 0 1.00223 1.41263i 0 0.260753 0.167576i 0 0.155773 + 0.0223967i 0 −0.991071 2.83157i 0
17.19 0 1.27658 1.17062i 0 −3.16079 + 2.03132i 0 −2.34525 0.337196i 0 0.259310 2.98877i 0
17.20 0 1.48588 + 0.890042i 0 1.88314 1.21022i 0 0.355050 + 0.0510485i 0 1.41565 + 2.64498i 0
See next 80 embeddings (of 240 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 521.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
23.d odd 22 1 inner
69.g even 22 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 552.2.u.a 240
3.b odd 2 1 inner 552.2.u.a 240
23.d odd 22 1 inner 552.2.u.a 240
69.g even 22 1 inner 552.2.u.a 240
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
552.2.u.a 240 1.a even 1 1 trivial
552.2.u.a 240 3.b odd 2 1 inner
552.2.u.a 240 23.d odd 22 1 inner
552.2.u.a 240 69.g even 22 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(552, [\chi])\).