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Properties

Label 455.2.cl.a
Level $455$
Weight $2$
Character orbit 455.cl
Analytic conductor $3.633$
Analytic rank $0$
Dimension $208$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [455,2,Mod(54,455)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("455.54"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(455, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 10, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 455 = 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 455.cl (of order \(12\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.63319329197\)
Analytic rank: \(0\)
Dimension: \(208\)
Relative dimension: \(52\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 208 q - 6 q^{5} + 24 q^{6} - 84 q^{9} - 6 q^{10} - 22 q^{15} - 168 q^{16} - 24 q^{19} + 12 q^{20} + 12 q^{21} + 36 q^{24} - 12 q^{26} - 20 q^{29} + 18 q^{30} - 12 q^{31} + 24 q^{34} - 4 q^{35} - 12 q^{36}+ \cdots - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
54.1 −1.97450 − 1.97450i −1.19666 + 2.07268i 5.79729i 2.22898 − 0.177927i 6.45531 − 1.72969i 0.795119 + 2.52345i 7.49775 − 7.49775i −1.36400 − 2.36251i −4.75243 − 4.04980i
54.2 −1.83748 − 1.83748i −0.230032 + 0.398427i 4.75268i −1.52820 + 1.63236i 1.15478 − 0.309423i −2.54879 − 0.709714i 5.05799 − 5.05799i 1.39417 + 2.41477i 5.80747 − 0.191407i
54.3 −1.79250 − 1.79250i 0.570210 − 0.987632i 4.42610i −0.848115 − 2.06899i −2.79243 + 0.748229i −0.864980 + 2.50036i 4.34877 − 4.34877i 0.849722 + 1.47176i −2.18841 + 5.22890i
54.4 −1.70582 − 1.70582i 0.876376 − 1.51793i 3.81963i −1.81559 + 1.30523i −4.08425 + 1.09437i 2.61783 − 0.383340i 3.10395 − 3.10395i −0.0360702 − 0.0624754i 5.32355 + 0.870576i
54.5 −1.67761 − 1.67761i −0.0710893 + 0.123130i 3.62875i 1.78039 + 1.35286i 0.325824 − 0.0873044i 0.569797 − 2.58367i 2.73241 − 2.73241i 1.48989 + 2.58057i −0.717231 − 5.25636i
54.6 −1.60002 − 1.60002i 1.00288 − 1.73704i 3.12010i 1.89456 − 1.18771i −4.38390 + 1.17466i 2.63857 + 0.194785i 1.79218 − 1.79218i −0.511527 − 0.885991i −4.93168 − 1.13096i
54.7 −1.53989 − 1.53989i −1.66747 + 2.88814i 2.74252i −2.10885 − 0.743462i 7.01514 − 1.87970i −2.50833 + 0.841606i 1.14339 − 1.14339i −4.06092 − 7.03372i 2.10255 + 4.39225i
54.8 −1.51836 − 1.51836i −0.942185 + 1.63191i 2.61081i 0.0390361 − 2.23573i 3.90840 − 1.04725i 1.05939 − 2.42439i 0.927434 − 0.927434i −0.275424 − 0.477048i −3.45390 + 3.33536i
54.9 −1.45992 − 1.45992i 1.52047 − 2.63354i 2.26275i −1.90616 − 1.16900i −6.06454 + 1.62499i −1.37796 − 2.25859i 0.383594 − 0.383594i −3.12369 − 5.41038i 1.07620 + 4.48949i
54.10 −1.35125 − 1.35125i −0.820812 + 1.42169i 1.65175i 0.449426 + 2.19044i 3.03018 − 0.811934i 1.09494 + 2.40855i −0.470569 + 0.470569i 0.152534 + 0.264197i 2.35254 − 3.56712i
54.11 −1.29511 − 1.29511i −1.43161 + 2.47962i 1.35463i −0.486590 + 2.18248i 5.06548 − 1.35729i 2.36022 − 1.19557i −0.835832 + 0.835832i −2.59902 − 4.50164i 3.45675 − 2.19637i
54.12 −1.28051 − 1.28051i 0.583111 − 1.00998i 1.27940i 1.72823 + 1.41889i −2.03996 + 0.546607i −2.10897 + 1.59758i −0.922731 + 0.922731i 0.819962 + 1.42022i −0.396112 − 4.02990i
54.13 −1.11196 − 1.11196i −0.266092 + 0.460885i 0.472893i −1.28746 − 1.82824i 0.808367 − 0.216601i 1.39754 + 2.24653i −1.69808 + 1.69808i 1.35839 + 2.35280i −0.601320 + 3.46452i
54.14 −0.966485 − 0.966485i 1.04990 − 1.81847i − 0.131813i 1.61919 − 1.54215i −2.77224 + 0.742818i −2.33151 − 1.25063i −2.06037 + 2.06037i −0.704563 − 1.22034i −3.05539 − 0.0744587i
54.15 −0.919959 − 0.919959i 0.136758 − 0.236872i − 0.307351i −2.23415 − 0.0925757i −0.343724 + 0.0921005i 1.54879 − 2.14505i −2.12267 + 2.12267i 1.46259 + 2.53329i 1.97016 + 2.14049i
54.16 −0.817444 − 0.817444i −0.603671 + 1.04559i − 0.663571i −2.14260 + 0.639737i 1.34818 − 0.361243i −1.82788 − 1.91281i −2.17732 + 2.17732i 0.771163 + 1.33569i 2.27441 + 1.22851i
54.17 −0.797919 − 0.797919i −0.779516 + 1.35016i − 0.726652i 0.969702 − 2.01486i 1.69931 − 0.455329i −1.90263 + 1.83848i −2.17565 + 2.17565i 0.284709 + 0.493131i −2.38144 + 0.833954i
54.18 −0.767371 − 0.767371i 0.697267 − 1.20770i − 0.822284i −1.61323 + 1.54839i −1.46182 + 0.391693i −1.33480 + 2.28436i −2.16574 + 2.16574i 0.527637 + 0.913893i 2.42613 + 0.0497575i
54.19 −0.617933 − 0.617933i 1.57245 − 2.72356i − 1.23632i 1.61913 + 1.54221i −2.65464 + 0.711309i 2.58422 + 0.567298i −1.99983 + 1.99983i −3.44518 − 5.96723i −0.0475314 − 1.95350i
54.20 −0.585058 − 0.585058i 1.49781 − 2.59428i − 1.31542i −1.85632 − 1.24663i −2.39410 + 0.641498i 0.832587 + 2.51133i −1.93971 + 1.93971i −2.98684 − 5.17336i 0.356702 + 1.81540i
See next 80 embeddings (of 208 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 54.52
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
91.ba even 12 1 inner
455.cl even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 455.2.cl.a ✓ 208
5.b even 2 1 inner 455.2.cl.a ✓ 208
7.d odd 6 1 455.2.dn.a yes 208
13.f odd 12 1 455.2.dn.a yes 208
35.i odd 6 1 455.2.dn.a yes 208
65.s odd 12 1 455.2.dn.a yes 208
91.ba even 12 1 inner 455.2.cl.a ✓ 208
455.cl even 12 1 inner 455.2.cl.a ✓ 208
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
455.2.cl.a ✓ 208 1.a even 1 1 trivial
455.2.cl.a ✓ 208 5.b even 2 1 inner
455.2.cl.a ✓ 208 91.ba even 12 1 inner
455.2.cl.a ✓ 208 455.cl even 12 1 inner
455.2.dn.a yes 208 7.d odd 6 1
455.2.dn.a yes 208 13.f odd 12 1
455.2.dn.a yes 208 35.i odd 6 1
455.2.dn.a yes 208 65.s odd 12 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(455, [\chi])\).