Properties

Label 460.2.j.a
Level $460$
Weight $2$
Character orbit 460.j
Analytic conductor $3.673$
Analytic rank $0$
Dimension $132$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(66\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 132q - 12q^{8} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 132q - 12q^{8} - 16q^{10} - 16q^{12} - 4q^{13} + 16q^{16} - 20q^{17} + 28q^{18} - 16q^{22} - 20q^{25} - 16q^{26} + 12q^{28} - 24q^{30} - 40q^{32} + 16q^{33} - 32q^{36} + 20q^{37} - 12q^{38} - 16q^{40} - 40q^{42} + 20q^{45} + 28q^{48} + 40q^{50} + 16q^{52} + 4q^{53} + 40q^{56} + 20q^{58} + 20q^{60} + 60q^{62} + 20q^{65} + 40q^{66} - 16q^{68} - 60q^{70} + 40q^{72} + 36q^{73} - 48q^{76} + 28q^{78} - 60q^{80} - 132q^{81} - 44q^{82} - 20q^{85} - 88q^{86} + 28q^{88} + 120q^{90} - 96q^{96} - 60q^{97} - 80q^{98} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
47.1 −1.41322 + 0.0530604i 1.60974 + 1.60974i 1.99437 0.149972i −1.92782 1.13292i −2.36032 2.18950i 1.60901 1.60901i −2.81052 + 0.317765i 2.18251i 2.78454 + 1.49877i
47.2 −1.41199 + 0.0791888i 0.613496 + 0.613496i 1.98746 0.223628i 0.184594 + 2.22844i −0.914836 0.817672i 1.46274 1.46274i −2.78857 + 0.473147i 2.24724i −0.437114 3.13192i
47.3 −1.40975 + 0.112316i −1.50989 1.50989i 1.97477 0.316673i −2.17152 + 0.533381i 2.29815 + 1.95898i 1.06422 1.06422i −2.74836 + 0.668226i 1.55955i 3.00139 0.995827i
47.4 −1.39809 0.212930i −0.766366 0.766366i 1.90932 + 0.595390i 2.12262 0.703182i 0.908268 + 1.23463i −1.45641 + 1.45641i −2.54263 1.23896i 1.82537i −3.11735 + 0.531143i
47.5 −1.38544 + 0.283802i 2.27633 + 2.27633i 1.83891 0.786383i 2.17204 + 0.531258i −3.79975 2.50770i 1.09581 1.09581i −2.32454 + 1.61138i 7.36333i −3.16002 0.119599i
47.6 −1.37758 0.319819i 0.818006 + 0.818006i 1.79543 + 0.881151i −0.0316596 + 2.23584i −0.865251 1.38848i −1.96436 + 1.96436i −2.19153 1.78807i 1.66173i 0.758679 3.06992i
47.7 −1.35036 + 0.420152i −2.31541 2.31541i 1.64695 1.13471i 0.145684 2.23132i 4.09946 + 2.15381i −1.71433 + 1.71433i −1.74722 + 2.22424i 7.72225i 0.740766 + 3.07429i
47.8 −1.34829 + 0.426761i 0.785861 + 0.785861i 1.63575 1.15079i −0.890562 2.05107i −1.39494 0.724190i −2.71252 + 2.71252i −1.71435 + 2.24967i 1.76485i 2.07605 + 2.38538i
47.9 −1.33173 0.475911i −1.70820 1.70820i 1.54702 + 1.26757i 1.45963 + 1.69395i 1.46191 + 3.08781i 3.00205 3.00205i −1.45696 2.42431i 2.83587i −1.13766 2.95055i
47.10 −1.30050 0.555604i −1.11072 1.11072i 1.38261 + 1.44513i −1.45914 1.69437i 0.827374 + 2.06162i 1.00241 1.00241i −0.995163 2.64757i 0.532591i 0.956214 + 3.01424i
47.11 −1.29378 + 0.571084i −0.0565025 0.0565025i 1.34773 1.47771i 2.13204 0.674090i 0.105369 + 0.0408341i 2.63515 2.63515i −0.899763 + 2.68150i 2.99361i −2.37343 + 2.08970i
47.12 −1.22458 0.707387i 1.89438 + 1.89438i 0.999207 + 1.73251i 1.67434 1.48208i −0.979766 3.65988i −2.51212 + 2.51212i 0.00194187 2.82843i 4.17735i −3.09878 + 0.630526i
47.13 −1.19633 + 0.754187i −0.274826 0.274826i 0.862404 1.80451i −2.10134 + 0.764452i 0.536053 + 0.121512i −0.802532 + 0.802532i 0.329221 + 2.80920i 2.84894i 1.93735 2.49934i
47.14 −1.19284 0.759687i 0.971542 + 0.971542i 0.845751 + 1.81238i 0.361417 2.20667i −0.420830 1.89697i 2.60162 2.60162i 0.367989 2.80439i 1.11221i −2.10749 + 2.35764i
47.15 −1.15450 0.816781i −2.22730 2.22730i 0.665738 + 1.88595i −0.469590 + 2.18620i 0.752200 + 4.39063i −3.32421 + 3.32421i 0.771810 2.72109i 6.92171i 2.32779 2.14042i
47.16 −1.12735 + 0.853866i −1.12763 1.12763i 0.541827 1.92521i 1.64258 + 1.51721i 2.23408 + 0.308387i −1.95321 + 1.95321i 1.03304 + 2.63303i 0.456898i −3.14725 0.307880i
47.17 −0.956422 + 1.04176i 1.18769 + 1.18769i −0.170514 1.99272i 1.54331 1.61809i −2.37321 + 0.101351i −0.438743 + 0.438743i 2.23901 + 1.72824i 0.178792i 0.209602 + 3.15532i
47.18 −0.865562 + 1.11839i −2.09555 2.09555i −0.501606 1.93608i −0.928013 + 2.03440i 4.15748 0.529822i 2.24593 2.24593i 2.59947 + 1.11480i 5.78270i −1.47201 2.79878i
47.19 −0.816781 1.15450i 2.22730 + 2.22730i −0.665738 + 1.88595i −0.469590 + 2.18620i 0.752200 4.39063i 3.32421 3.32421i 2.72109 0.771810i 6.92171i 2.90752 1.24351i
47.20 −0.759687 1.19284i −0.971542 0.971542i −0.845751 + 1.81238i 0.361417 2.20667i −0.420830 + 1.89697i −2.60162 + 2.60162i 2.80439 0.367989i 1.11221i −2.90677 + 1.24526i
See next 80 embeddings (of 132 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 323.66
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 460.2.j.a 132
4.b odd 2 1 inner 460.2.j.a 132
5.c odd 4 1 inner 460.2.j.a 132
20.e even 4 1 inner 460.2.j.a 132
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
460.2.j.a 132 1.a even 1 1 trivial
460.2.j.a 132 4.b odd 2 1 inner
460.2.j.a 132 5.c odd 4 1 inner
460.2.j.a 132 20.e even 4 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(460, [\chi])\).