Properties

Label 460.2.x.a
Level $460$
Weight $2$
Character orbit 460.x
Analytic conductor $3.673$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.x (of order \(44\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 240q + 4q^{3} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 240q + 4q^{3} - 8q^{13} + 46q^{23} - 24q^{25} - 20q^{27} + 12q^{31} + 22q^{33} + 4q^{35} - 88q^{37} + 12q^{41} - 92q^{47} - 36q^{55} - 88q^{57} + 88q^{61} + 168q^{71} + 20q^{73} + 12q^{75} + 36q^{77} + 200q^{81} - 28q^{85} + 16q^{87} - 88q^{93} - 86q^{95} - 66q^{97} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 0 −2.71854 + 1.48444i 0 1.97074 + 1.05650i 0 2.65480 + 3.54640i 0 3.56500 5.54725i 0
17.2 0 −1.95329 + 1.06658i 0 0.617840 2.14902i 0 0.0518807 + 0.0693045i 0 1.05584 1.64292i 0
17.3 0 −1.92230 + 1.04965i 0 0.766931 + 2.10043i 0 −2.30217 3.07534i 0 0.971534 1.51174i 0
17.4 0 −1.47141 + 0.803448i 0 −1.48903 1.66817i 0 0.330540 + 0.441549i 0 −0.102418 + 0.159366i 0
17.5 0 −1.02467 + 0.559510i 0 2.07680 0.828788i 0 −2.22248 2.96889i 0 −0.885033 + 1.37714i 0
17.6 0 0.302476 0.165164i 0 0.209636 + 2.22622i 0 1.78504 + 2.38454i 0 −1.55771 + 2.42384i 0
17.7 0 0.416910 0.227650i 0 −2.14737 0.623543i 0 −0.887718 1.18585i 0 −1.49993 + 2.33394i 0
17.8 0 0.483512 0.264018i 0 −0.935821 + 2.03082i 0 −1.13426 1.51520i 0 −1.45784 + 2.26845i 0
17.9 0 0.707493 0.386321i 0 1.31269 1.81021i 0 2.84997 + 3.80711i 0 −1.27062 + 1.97712i 0
17.10 0 1.92117 1.04904i 0 −0.336864 2.21055i 0 −2.02919 2.71068i 0 0.968479 1.50698i 0
17.11 0 2.20798 1.20565i 0 1.99649 + 1.00699i 0 −0.375619 0.501768i 0 1.79966 2.80032i 0
17.12 0 2.69738 1.47288i 0 −2.20694 + 0.359751i 0 2.19560 + 2.93298i 0 3.48456 5.42208i 0
33.1 0 −0.632093 2.90569i 0 −1.58894 1.57330i 0 0.867718 + 1.58911i 0 −5.31457 + 2.42708i 0
33.2 0 −0.486808 2.23782i 0 0.0638162 + 2.23516i 0 1.23306 + 2.25818i 0 −2.04197 + 0.932535i 0
33.3 0 −0.409167 1.88091i 0 2.14867 + 0.619038i 0 −1.26125 2.30981i 0 −0.641504 + 0.292965i 0
33.4 0 −0.299812 1.37822i 0 0.675503 2.13159i 0 −0.759843 1.39155i 0 0.919306 0.419833i 0
33.5 0 −0.0813911 0.374149i 0 −2.18808 0.460771i 0 0.364123 + 0.666841i 0 2.59553 1.18534i 0
33.6 0 0.0980316 + 0.450644i 0 2.20605 0.365176i 0 1.83859 + 3.36712i 0 2.53543 1.15789i 0
33.7 0 0.132785 + 0.610405i 0 −1.61522 + 1.54631i 0 −2.27438 4.16522i 0 2.37393 1.08414i 0
33.8 0 0.195370 + 0.898100i 0 −2.15927 0.580987i 0 1.50914 + 2.76379i 0 1.96048 0.895322i 0
See next 80 embeddings (of 240 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 457.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
23.d odd 22 1 inner
115.l even 44 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 460.2.x.a 240
5.c odd 4 1 inner 460.2.x.a 240
23.d odd 22 1 inner 460.2.x.a 240
115.l even 44 1 inner 460.2.x.a 240
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
460.2.x.a 240 1.a even 1 1 trivial
460.2.x.a 240 5.c odd 4 1 inner
460.2.x.a 240 23.d odd 22 1 inner
460.2.x.a 240 115.l even 44 1 inner

Hecke kernels

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