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Properties

Label 280.2.br.a
Level $280$
Weight $2$
Character orbit 280.br
Analytic conductor $2.236$
Analytic rank $0$
Dimension $176$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [280,2,Mod(67,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 6, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.br (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(176\)
Relative dimension: \(44\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
67.1 −1.41382 − 0.0333641i 0.388267 + 1.44903i 1.99777 + 0.0943417i 2.17362 − 0.524773i −0.500594 − 2.06162i 2.60799 − 0.445401i −2.82134 − 0.200036i 0.649136 − 0.374779i −3.09061 + 0.669413i
67.2 −1.41151 + 0.0874515i −0.147176 − 0.549269i 1.98470 − 0.246877i −1.31051 + 1.81179i 0.255774 + 0.762426i 0.374780 − 2.61907i −2.77983 + 0.522034i 2.31804 − 1.33832i 1.69135 − 2.67196i
67.3 −1.38856 + 0.268130i 0.262906 + 0.981180i 1.85621 − 0.744631i −1.42407 − 1.72396i −0.628146 − 1.29194i 0.0598247 + 2.64507i −2.37781 + 1.53167i 1.70448 − 0.984083i 2.43965 + 2.01199i
67.4 −1.38301 − 0.295435i −0.482920 − 1.80228i 1.82544 + 0.817180i 0.915641 − 2.04000i 0.135426 + 2.63525i −2.62546 − 0.327068i −2.28317 − 1.66947i −0.416933 + 0.240716i −1.86903 + 2.55083i
67.5 −1.32896 + 0.483609i 0.835437 + 3.11790i 1.53224 − 1.28539i 0.804876 + 2.08619i −2.61810 − 3.73952i −2.64531 + 0.0485395i −1.41466 + 2.44923i −6.42524 + 3.70961i −2.07854 − 2.38320i
67.6 −1.32319 − 0.499155i −0.833838 − 3.11193i 1.50169 + 1.32096i −2.20028 + 0.398453i −0.450005 + 4.53390i 1.42374 + 2.23002i −1.32766 − 2.49746i −6.39072 + 3.68968i 3.11029 + 0.571051i
67.7 −1.24593 + 0.669082i −0.569871 − 2.12679i 1.10466 − 1.66725i 2.01915 + 0.960747i 2.13301 + 2.26853i 0.895661 + 2.48954i −0.260793 + 2.81638i −1.60039 + 0.923986i −3.15853 + 0.153958i
67.8 −1.18837 − 0.766666i 0.205610 + 0.767348i 0.824448 + 1.82217i 1.68075 + 1.47481i 0.343958 − 1.06953i −2.28076 + 1.34095i 0.417242 − 2.79748i 2.05153 − 1.18445i −0.866669 − 3.04120i
67.9 −1.17517 − 0.786756i 0.673346 + 2.51296i 0.762030 + 1.84914i −1.71938 + 1.42959i 1.18579 − 3.48291i 2.61222 + 0.419863i 0.559308 − 2.77258i −3.26351 + 1.88419i 3.14530 − 0.327278i
67.10 −1.16325 + 0.804274i −0.540340 − 2.01658i 0.706287 − 1.87114i 0.161306 − 2.23024i 2.25043 + 1.91120i 1.67330 − 2.04940i 0.683321 + 2.74464i −1.17654 + 0.679275i 1.60609 + 2.72406i
67.11 −1.04840 + 0.949136i −0.0956638 − 0.357022i 0.198283 − 1.99015i −1.68428 + 1.47078i 0.439157 + 0.283504i −2.10200 + 1.60674i 1.68104 + 2.27467i 2.47976 − 1.43169i 0.369825 − 3.14058i
67.12 −0.986956 − 1.01288i −0.565335 − 2.10986i −0.0518375 + 1.99933i 1.71378 + 1.43630i −1.57907 + 2.65495i 1.45748 − 2.20811i 2.07623 − 1.92074i −1.53383 + 0.885555i −0.236634 − 3.15341i
67.13 −0.942490 + 1.05438i 0.438259 + 1.63560i −0.223426 − 1.98748i −0.615814 − 2.14960i −2.13760 − 1.07945i −0.885584 − 2.49314i 2.30613 + 1.63760i 0.114945 − 0.0663635i 2.84689 + 1.37667i
67.14 −0.786782 − 1.17515i 0.552175 + 2.06075i −0.761947 + 1.84917i 1.28687 − 1.82865i 1.98724 − 2.27025i −0.126396 − 2.64273i 2.77254 − 0.559495i −1.34370 + 0.775786i −3.16142 − 0.0735182i
67.15 −0.784588 − 1.17661i −0.0488512 − 0.182315i −0.768843 + 1.84632i −0.546472 − 2.16826i −0.176187 + 0.200521i 1.82312 + 1.91735i 2.77563 − 0.543964i 2.56722 − 1.48219i −2.12246 + 2.34418i
67.16 −0.624657 + 1.26878i 0.629416 + 2.34901i −1.21961 − 1.58511i 1.82068 − 1.29812i −3.37355 − 0.668737i 0.511566 + 2.59582i 2.77299 − 0.557266i −2.52362 + 1.45701i 0.509724 + 3.12093i
67.17 −0.431412 − 1.34680i −0.409884 − 1.52971i −1.62777 + 1.16206i −2.22655 − 0.206144i −1.88339 + 1.21197i −2.08935 − 1.62314i 2.26730 + 1.69096i 0.426076 − 0.245995i 0.682924 + 3.08766i
67.18 −0.421789 + 1.34985i −0.220018 − 0.821117i −1.64419 − 1.13870i 2.20849 + 0.350108i 1.20119 + 0.0493476i −2.38534 − 1.14463i 2.23058 − 1.73911i 1.97225 − 1.13868i −1.40411 + 2.83346i
67.19 −0.309645 + 1.37990i −0.220018 − 0.821117i −1.80824 − 0.854556i −2.20849 − 0.350108i 1.20119 − 0.0493476i 2.38534 + 1.14463i 1.73911 − 2.23058i 1.97225 − 1.13868i 1.16696 − 2.93908i
67.20 −0.110222 − 1.40991i 0.0164275 + 0.0613082i −1.97570 + 0.310806i −0.336260 + 2.21064i 0.0846285 − 0.0299188i 2.52833 + 0.779437i 0.655974 + 2.75131i 2.59459 − 1.49799i 3.15387 + 0.230436i
See next 80 embeddings (of 176 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 67.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
7.c even 3 1 inner
8.d odd 2 1 inner
35.l odd 12 1 inner
40.k even 4 1 inner
56.k odd 6 1 inner
280.br even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 280.2.br.a ✓ 176
5.c odd 4 1 inner 280.2.br.a ✓ 176
7.c even 3 1 inner 280.2.br.a ✓ 176
8.d odd 2 1 inner 280.2.br.a ✓ 176
35.l odd 12 1 inner 280.2.br.a ✓ 176
40.k even 4 1 inner 280.2.br.a ✓ 176
56.k odd 6 1 inner 280.2.br.a ✓ 176
280.br even 12 1 inner 280.2.br.a ✓ 176
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.2.br.a ✓ 176 1.a even 1 1 trivial
280.2.br.a ✓ 176 5.c odd 4 1 inner
280.2.br.a ✓ 176 7.c even 3 1 inner
280.2.br.a ✓ 176 8.d odd 2 1 inner
280.2.br.a ✓ 176 35.l odd 12 1 inner
280.2.br.a ✓ 176 40.k even 4 1 inner
280.2.br.a ✓ 176 56.k odd 6 1 inner
280.2.br.a ✓ 176 280.br even 12 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(280, [\chi])\).