Properties

Label 275.3.v.b
Level $275$
Weight $3$
Character orbit 275.v
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(21,275)] 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("275.21"); 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([6, 5])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 275.v (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.

\(\operatorname{Tr}(f)(q) = \) \( 224 q - 18 q^{3} + 114 q^{4} + 10 q^{5} - 146 q^{9} - 40 q^{11} + 98 q^{12} + 18 q^{14} - 30 q^{15} - 78 q^{16} + 10 q^{20} - 120 q^{22} + 142 q^{23} + 350 q^{25} + 68 q^{26} + 276 q^{27} - 230 q^{31} + 32 q^{33}+ \cdots + 840 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
21.1 −3.77431 − 1.22635i −1.46129 − 1.06169i 9.50540 + 6.90608i −3.61160 + 3.45780i 4.21336 + 5.79920i − 2.71304i −18.0764 − 24.8801i −1.77297 − 5.45663i 17.8717 − 8.62171i
21.2 −3.60637 − 1.17178i 3.49716 + 2.54084i 8.39676 + 6.10060i −4.22850 − 2.66830i −9.63475 − 13.2611i 7.39934i −14.2178 − 19.5691i 2.99313 + 9.21191i 12.1229 + 14.5777i
21.3 −3.56024 − 1.15679i −2.57947 − 1.87409i 8.10108 + 5.88578i 3.04782 − 3.96369i 7.01560 + 9.65614i 11.8181i −13.2318 − 18.2120i 0.360280 + 1.10883i −15.4361 + 10.5860i
21.4 −3.25554 − 1.05779i 1.93617 + 1.40671i 6.24356 + 4.53621i −0.329633 − 4.98912i −4.81527 − 6.62765i − 13.1581i −7.47968 − 10.2949i −1.01124 − 3.11227i −4.20431 + 16.5910i
21.5 −3.22741 − 1.04865i 1.10252 + 0.801031i 6.08047 + 4.41772i 3.28412 + 3.77022i −2.71830 − 3.74142i − 1.83974i −7.01293 − 9.65247i −2.20724 − 6.79320i −6.64559 − 15.6119i
21.6 −3.20580 − 1.04163i 0.536695 + 0.389931i 5.95610 + 4.32736i 4.81272 − 1.35563i −1.31437 − 1.80908i − 1.73701i −6.66140 − 9.16863i −2.64516 − 8.14096i −16.8407 − 0.667169i
21.7 −3.14218 − 1.02096i −4.31054 − 3.13179i 5.59487 + 4.06491i 4.34369 + 2.47637i 10.3471 + 14.2415i − 7.85039i −5.66209 − 7.79320i 5.99149 + 18.4399i −11.1204 − 12.2159i
21.8 −3.03705 − 0.986797i 2.87023 + 2.08534i 5.01384 + 3.64276i −0.638506 + 4.95906i −6.65921 − 9.16562i 8.01657i −4.12460 − 5.67702i 1.10840 + 3.41130i 6.83276 − 14.4308i
21.9 −2.97566 − 0.966849i −4.05897 − 2.94901i 4.68367 + 3.40288i −3.96306 − 3.04864i 9.22684 + 12.6997i − 5.63426i −3.29068 − 4.52924i 4.99738 + 15.3804i 8.84513 + 12.9034i
21.10 −2.73603 − 0.888990i −1.08856 − 0.790888i 3.45948 + 2.51346i −2.58198 − 4.28175i 2.27525 + 3.13162i 2.26906i −0.466973 − 0.642733i −2.22169 − 6.83764i 3.25793 + 14.0103i
21.11 −2.62627 − 0.853326i −2.56722 − 1.86519i 2.93305 + 2.13098i −2.87038 + 4.09401i 5.15059 + 7.08917i 7.34029i 0.607948 + 0.836769i 0.330515 + 1.01722i 11.0319 − 8.30260i
21.12 −2.51375 − 0.816767i 3.35285 + 2.43599i 2.41577 + 1.75516i −4.55205 + 2.06853i −6.43859 − 8.86196i − 7.24566i 1.57525 + 2.16814i 2.52640 + 7.77547i 13.1322 − 1.48180i
21.13 −2.44398 − 0.794099i 4.17370 + 3.03237i 2.10640 + 1.53039i 3.04154 − 3.96851i −7.79246 − 10.7254i 4.11109i 2.10914 + 2.90298i 5.44335 + 16.7529i −10.5849 + 7.28369i
21.14 −2.03827 − 0.662275i −1.06311 − 0.772397i 0.479876 + 0.348651i 0.240315 + 4.99422i 1.65537 + 2.27843i − 11.9123i 4.29167 + 5.90698i −2.24754 − 6.91722i 2.81772 − 10.3387i
21.15 −1.93753 − 0.629542i 0.694190 + 0.504359i 0.121632 + 0.0883706i −4.78862 − 1.43844i −1.02750 − 1.41423i 7.71321i 4.60981 + 6.34485i −2.55363 − 7.85927i 8.37254 + 5.80165i
21.16 −1.92419 − 0.625206i −2.09482 − 1.52197i 0.0755390 + 0.0548823i 4.97269 − 0.521889i 3.07927 + 4.23825i 0.492154i 4.64581 + 6.39441i −0.709299 − 2.18300i −9.89466 − 2.10474i
21.17 −1.80801 − 0.587458i 4.10843 + 2.98495i −0.312279 − 0.226884i 4.16682 + 2.76362i −5.67455 − 7.81034i − 4.69830i 4.90096 + 6.74560i 5.18812 + 15.9674i −5.91014 − 7.44448i
21.18 −1.69488 − 0.550698i −1.89854 − 1.37937i −0.666734 − 0.484411i 3.49907 − 3.57163i 2.45817 + 3.38338i − 7.59066i 5.05323 + 6.95517i −1.07936 − 3.32193i −7.89737 + 4.12653i
21.19 −1.64576 − 0.534739i 0.504907 + 0.366837i −0.813492 − 0.591037i 4.05133 + 2.93032i −0.634794 − 0.873719i 11.8380i 5.09130 + 7.00757i −2.66079 − 8.18907i −5.10055 − 6.98900i
21.20 −1.40543 − 0.456653i 2.11905 + 1.53958i −1.46936 − 1.06755i 0.918638 − 4.91489i −2.27513 − 3.13144i 2.87031i 5.05200 + 6.95349i −0.661088 − 2.03462i −3.53548 + 6.48804i
See next 80 embeddings (of 224 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 21.56
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.d even 5 1 inner
275.v 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.v.b ✓ 224
11.b odd 2 1 inner 275.3.v.b ✓ 224
25.d even 5 1 inner 275.3.v.b ✓ 224
275.v odd 10 1 inner 275.3.v.b ✓ 224
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
275.3.v.b ✓ 224 1.a even 1 1 trivial
275.3.v.b ✓ 224 11.b odd 2 1 inner
275.3.v.b ✓ 224 25.d even 5 1 inner
275.3.v.b ✓ 224 275.v odd 10 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{224} - 169 T_{2}^{222} + 15120 T_{2}^{220} - 952560 T_{2}^{218} + 47443260 T_{2}^{216} + \cdots + 14\!\cdots\!25 \) acting on \(S_{3}^{\mathrm{new}}(275, [\chi])\). Copy content Toggle raw display