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Properties

Label 935.2.bv.a
Level $935$
Weight $2$
Character orbit 935.bv
Analytic conductor $7.466$
Analytic rank $0$
Dimension $832$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [935,2,Mod(123,935)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(935, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([15, 2, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("935.123");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 935.bv (of order \(20\), degree \(8\), 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: \(7.46601258899\)
Analytic rank: \(0\)
Dimension: \(832\)
Relative dimension: \(104\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 832 q - 12 q^{3} - 2 q^{5} - 20 q^{6} - 40 q^{7} - 216 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 832 q - 12 q^{3} - 2 q^{5} - 20 q^{6} - 40 q^{7} - 216 q^{9} - 12 q^{11} - 20 q^{13} - 24 q^{14} + 32 q^{15} + 160 q^{16} - 20 q^{18} - 26 q^{20} + 40 q^{24} - 12 q^{25} + 12 q^{27} - 20 q^{30} - 28 q^{31} - 12 q^{33} - 20 q^{35} - 28 q^{38} + 80 q^{39} - 120 q^{40} - 20 q^{41} - 24 q^{42} + 24 q^{44} + 36 q^{45} + 20 q^{46} - 12 q^{47} + 92 q^{48} + 160 q^{49} - 20 q^{50} - 100 q^{51} - 100 q^{52} - 32 q^{56} - 100 q^{57} - 32 q^{59} + 84 q^{60} + 20 q^{61} - 320 q^{62} + 140 q^{63} - 32 q^{67} - 70 q^{68} + 84 q^{70} - 60 q^{71} - 20 q^{72} - 20 q^{73} - 26 q^{75} - 32 q^{77} + 40 q^{79} - 76 q^{80} - 144 q^{81} - 50 q^{85} - 24 q^{86} + 84 q^{88} + 60 q^{90} + 56 q^{91} + 244 q^{92} + 24 q^{93} - 20 q^{96} + 4 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
123.1 −1.26441 − 2.48154i 1.31484 − 0.955286i −3.38372 + 4.65730i 1.96652 − 1.06432i −4.03306 − 2.05495i 1.72644 − 2.37624i 10.3340 + 1.63675i −0.110823 + 0.341077i −5.12764 − 3.53426i
123.2 −1.26056 − 2.47398i −1.37212 + 0.996906i −3.35601 + 4.61916i −1.95070 − 1.09306i 4.19597 + 2.13795i −0.820842 + 1.12979i 10.1733 + 1.61129i −0.0381495 + 0.117412i −0.245234 + 6.20386i
123.3 −1.22583 − 2.40584i −2.29420 + 1.66683i −3.10981 + 4.28028i 2.03337 − 0.930282i 6.82243 + 3.47620i 0.0316493 − 0.0435615i 8.77598 + 1.38998i 1.55796 − 4.79492i −4.73068 − 3.75157i
123.4 −1.17374 − 2.30359i 0.692359 − 0.503028i −2.75330 + 3.78960i 2.21511 − 0.305454i −1.97142 − 1.00449i −2.81920 + 3.88030i 6.85424 + 1.08560i −0.700727 + 2.15662i −3.30360 − 4.74418i
123.5 −1.15673 − 2.27022i 0.132616 − 0.0963512i −2.64029 + 3.63405i 0.589258 + 2.15703i −0.372140 − 0.189615i 1.31066 − 1.80396i 6.27109 + 0.993243i −0.918748 + 2.82761i 4.21531 − 3.83286i
123.6 −1.15289 − 2.26268i 2.07494 − 1.50753i −2.61498 + 3.59921i 0.930165 + 2.03342i −5.80324 − 2.95690i −1.32529 + 1.82410i 6.14226 + 0.972838i 1.10567 − 3.40290i 3.52859 − 4.44898i
123.7 −1.15168 − 2.26031i 1.72244 − 1.25142i −2.60703 + 3.58828i −1.72799 − 1.41918i −4.81230 − 2.45199i −1.08844 + 1.49811i 6.10194 + 0.966452i 0.473675 − 1.45782i −1.21768 + 5.54022i
123.8 −1.15019 − 2.25738i 2.49664 − 1.81392i −2.59726 + 3.57483i −1.95760 + 1.08065i −6.96633 − 3.54952i 1.10512 − 1.52107i 6.05245 + 0.958614i 2.01588 − 6.20423i 4.69106 + 3.17610i
123.9 −1.10456 − 2.16781i −0.437776 + 0.318063i −2.30380 + 3.17090i −1.97116 + 1.05572i 1.17305 + 0.597698i −1.00884 + 1.38855i 4.61252 + 0.730551i −0.836567 + 2.57469i 4.46585 + 3.10700i
123.10 −1.08849 − 2.13629i −1.61393 + 1.17259i −2.20333 + 3.03262i 1.35710 + 1.77715i 4.26173 + 2.17146i −2.55391 + 3.51515i 4.14067 + 0.655818i 0.302755 − 0.931783i 2.31931 − 4.83357i
123.11 −1.05538 − 2.07130i −1.81325 + 1.31740i −2.00090 + 2.75400i −2.15581 − 0.593705i 4.64240 + 2.36542i 2.81735 − 3.87775i 3.22396 + 0.510626i 0.625266 − 1.92437i 1.04546 + 5.09192i
123.12 −1.05106 − 2.06283i 0.0553109 − 0.0401857i −1.97495 + 2.71828i 0.0353017 − 2.23579i −0.141031 − 0.0718591i −0.502060 + 0.691027i 3.10981 + 0.492546i −0.925607 + 2.84872i −4.64915 + 2.27713i
123.13 −1.04680 − 2.05446i −0.856467 + 0.622260i −1.94943 + 2.68316i 0.0582888 − 2.23531i 2.17495 + 1.10819i 1.99746 − 2.74926i 2.99833 + 0.474890i −0.580722 + 1.78728i −4.65336 + 2.22016i
123.14 −1.04430 − 2.04955i −2.57077 + 1.86777i −1.93453 + 2.66265i −1.03381 + 1.98273i 6.51274 + 3.31841i −0.619445 + 0.852593i 2.93359 + 0.464634i 2.19322 − 6.75004i 5.14332 + 0.0482869i
123.15 −1.01602 − 1.99406i 0.629013 − 0.457005i −1.76839 + 2.43398i −1.78123 + 1.35174i −1.55038 − 0.789960i 1.74303 − 2.39908i 2.22935 + 0.353094i −0.740247 + 2.27825i 4.50522 + 2.17848i
123.16 −0.986131 − 1.93539i −1.20976 + 0.878941i −1.59771 + 2.19907i 2.22841 + 0.184950i 2.89408 + 1.47461i 1.18918 − 1.63677i 1.54081 + 0.244041i −0.236072 + 0.726556i −1.83955 − 4.49522i
123.17 −0.929952 − 1.82513i 2.08122 − 1.51209i −1.29073 + 1.77654i 2.23374 + 0.101976i −4.69520 − 2.39232i 2.75123 − 3.78674i 0.396383 + 0.0627809i 1.11799 − 3.44082i −1.89115 − 4.17171i
123.18 −0.894196 − 1.75496i 1.69283 − 1.22991i −1.10472 + 1.52052i 0.449616 + 2.19040i −3.67217 − 1.87106i −1.54096 + 2.12095i −0.234485 − 0.0371388i 0.425934 − 1.31089i 3.44201 − 2.74770i
123.19 −0.892368 − 1.75137i 1.65418 − 1.20183i −1.09541 + 1.50770i 0.802473 − 2.08711i −3.58099 − 1.82460i 0.378645 − 0.521161i −0.264774 − 0.0419361i 0.364858 − 1.12292i −4.37141 + 0.457045i
123.20 −0.877211 − 1.72162i 1.21350 − 0.881661i −1.01892 + 1.40242i −2.11027 − 0.739440i −2.58239 − 1.31579i −2.02400 + 2.78580i −0.508624 − 0.0805582i −0.231790 + 0.713375i 0.578113 + 4.28173i
See next 80 embeddings (of 832 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 123.104
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.d odd 10 1 inner
85.i odd 4 1 inner
935.bv even 20 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 935.2.bv.a ✓ 832
5.c odd 4 1 935.2.ca.a yes 832
11.d odd 10 1 inner 935.2.bv.a ✓ 832
17.c even 4 1 935.2.ca.a yes 832
55.l even 20 1 935.2.ca.a yes 832
85.i odd 4 1 inner 935.2.bv.a ✓ 832
187.o odd 20 1 935.2.ca.a yes 832
935.bv even 20 1 inner 935.2.bv.a ✓ 832
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
935.2.bv.a ✓ 832 1.a even 1 1 trivial
935.2.bv.a ✓ 832 11.d odd 10 1 inner
935.2.bv.a ✓ 832 85.i odd 4 1 inner
935.2.bv.a ✓ 832 935.bv even 20 1 inner
935.2.ca.a yes 832 5.c odd 4 1
935.2.ca.a yes 832 17.c even 4 1
935.2.ca.a yes 832 55.l even 20 1
935.2.ca.a yes 832 187.o odd 20 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(935, [\chi])\).