Properties

Label 275.3.s.b
Level $275$
Weight $3$
Character orbit 275.s
Analytic conductor $7.493$
Analytic rank $0$
Dimension $224$
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [275,3,Mod(54,275)] 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("275.54"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([1, 5])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 275.s (of order \(10\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [224] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.49320726991\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(56\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 224 q - 10 q^{3} - 126 q^{4} - 22 q^{5} + 142 q^{9} + 34 q^{11} - 70 q^{12} - 30 q^{14} - 94 q^{15} - 286 q^{16} + 58 q^{20} + 110 q^{22} - 170 q^{23} + 78 q^{25} - 100 q^{26} + 260 q^{27} + 218 q^{31}+ \cdots + 1112 q^{99}+O(q^{100}) \) 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 −1.17743 + 3.62375i −1.63952 + 2.25661i −8.50918 − 6.18228i 0.893997 + 4.91943i −6.24697 − 8.59822i −11.5744 20.0918 − 14.5975i 0.376905 + 1.15999i −18.8794 − 2.55265i
54.2 −1.16104 + 3.57332i −3.02257 + 4.16021i −8.18452 − 5.94640i 2.33525 − 4.42115i −11.3564 − 15.6308i 2.24623 18.5924 − 13.5081i −5.39028 − 16.5896i 13.0869 + 13.4777i
54.3 −1.14349 + 3.51929i −0.561371 + 0.772661i −7.84180 − 5.69740i −4.47391 − 2.23252i −2.07730 − 2.85916i 3.91934 17.0431 − 12.3825i 2.49929 + 7.69201i 12.9728 − 13.1921i
54.4 −1.10427 + 3.39858i 3.02726 − 4.16666i −7.09489 − 5.15474i −3.83194 + 3.21188i 10.8178 + 14.8895i 1.54647 13.7894 − 10.0186i −5.41563 − 16.6676i −6.68437 − 16.5700i
54.5 −1.09648 + 3.37462i 1.44920 − 1.99465i −6.94974 − 5.04928i −1.39715 − 4.80083i 5.14217 + 7.07759i −3.76749 13.1772 − 9.57378i 0.902703 + 2.77823i 17.7329 + 0.549180i
54.6 −1.08330 + 3.33406i 2.39835 − 3.30104i −6.70634 − 4.87244i 4.94259 + 0.755493i 8.40774 + 11.5723i −3.99708 12.1655 − 8.83876i −2.36366 − 7.27461i −7.87318 + 15.6605i
54.7 −1.06803 + 3.28705i 0.0284510 − 0.0391595i −6.42794 − 4.67017i 0.164269 + 4.99730i 0.0983326 + 0.135343i 11.5143 11.0318 − 8.01504i 2.78043 + 8.55728i −16.6018 − 4.79729i
54.8 −0.919451 + 2.82978i −1.06200 + 1.46172i −3.92619 − 2.85255i 4.89026 + 1.04179i −3.15989 − 4.34922i −2.36176 2.05340 − 1.49188i 1.77237 + 5.45480i −7.44438 + 12.8805i
54.9 −0.872434 + 2.68508i −1.33084 + 1.83174i −3.21242 − 2.33396i 4.27275 − 2.59684i −3.75730 − 5.17148i 7.29579 −0.0667635 + 0.0485065i 1.19700 + 3.68400i 3.24503 + 13.7382i
54.10 −0.865381 + 2.66337i −2.50910 + 3.45347i −3.10858 − 2.25852i −4.90667 − 0.961579i −7.02655 − 9.67122i −9.68675 −0.357019 + 0.259389i −2.84977 − 8.77069i 6.80717 − 12.2361i
54.11 −0.847470 + 2.60824i −3.44081 + 4.73587i −2.84866 − 2.06967i −1.34569 + 4.81551i −9.43632 − 12.9880i 9.44212 −1.06245 + 0.771918i −7.80813 − 24.0309i −11.4196 − 7.59089i
54.12 −0.841199 + 2.58894i 0.253624 − 0.349084i −2.75895 − 2.00449i 1.38602 − 4.80405i 0.690410 + 0.950268i −9.46676 −1.29881 + 0.943642i 2.72362 + 8.38244i 11.2715 + 7.62950i
54.13 −0.824352 + 2.53710i 2.38064 − 3.27667i −2.52123 − 1.83178i 1.71428 − 4.69694i 6.35073 + 8.74103i 12.5247 −1.90695 + 1.38548i −2.28796 − 7.04162i 10.5034 + 8.22122i
54.14 −0.789134 + 2.42870i −0.901355 + 1.24061i −2.03980 − 1.48200i −4.83231 + 1.28405i −2.30178 − 3.16813i 2.13585 −3.05490 + 2.21951i 2.05448 + 6.32305i 0.694758 − 12.7495i
54.15 −0.705749 + 2.17207i 1.83741 − 2.52898i −0.983747 − 0.714734i 2.90075 + 4.07255i 4.19637 + 5.77581i −1.89314 −5.14397 + 3.73731i −0.238504 − 0.734039i −10.8931 + 3.42644i
54.16 −0.671958 + 2.06807i 1.01040 − 1.39069i −0.589334 − 0.428176i −2.02116 + 4.57328i 2.19711 + 3.02407i −8.69200 −5.75533 + 4.18149i 1.86803 + 5.74920i −8.09975 − 7.25296i
54.17 −0.655034 + 2.01599i 2.04574 − 2.81571i −0.399069 − 0.289941i −4.99184 − 0.285501i 4.33642 + 5.96857i 6.37032 −6.01369 + 4.36920i −0.962055 − 2.96090i 3.84539 − 9.87648i
54.18 −0.521156 + 1.60395i 3.25149 − 4.47530i 0.935004 + 0.679320i −3.99536 − 3.00618i 5.48363 + 7.54757i −11.6008 −7.03450 + 5.11086i −6.67492 − 20.5433i 6.90398 − 4.84167i
54.19 −0.503044 + 1.54821i −2.68640 + 3.69751i 1.09216 + 0.793504i −1.46946 − 4.77919i −4.37314 − 6.01912i −0.148995 −7.04587 + 5.11912i −3.67368 − 11.3064i 8.13840 + 0.129109i
54.20 −0.413102 + 1.27140i −2.03859 + 2.80588i 1.79027 + 1.30071i 1.17419 + 4.86017i −2.72524 − 3.75097i −2.68597 −6.71934 + 4.88189i −0.935951 − 2.88056i −6.66427 − 0.514879i
See next 80 embeddings (of 224 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 54.56
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.b odd 2 1 inner
25.e even 10 1 inner
275.s odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 275.3.s.b ✓ 224
11.b odd 2 1 inner 275.3.s.b ✓ 224
25.e even 10 1 inner 275.3.s.b ✓ 224
275.s odd 10 1 inner 275.3.s.b ✓ 224
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
275.3.s.b ✓ 224 1.a even 1 1 trivial
275.3.s.b ✓ 224 11.b odd 2 1 inner
275.3.s.b ✓ 224 25.e even 10 1 inner
275.3.s.b ✓ 224 275.s odd 10 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{224} + 175 T_{2}^{222} + 16180 T_{2}^{220} + 1051940 T_{2}^{218} + 54003500 T_{2}^{216} + \cdots + 38\!\cdots\!25 \) acting on \(S_{3}^{\mathrm{new}}(275, [\chi])\). Copy content Toggle raw display