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Properties

Label 201.3.o.b
Level $201$
Weight $3$
Character orbit 201.o
Analytic conductor $5.477$
Analytic rank $0$
Dimension $840$
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] = [201,3,Mod(17,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([33, 64]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.o (of order \(66\), degree \(20\), 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: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(840\)
Relative dimension: \(42\) over \(\Q(\zeta_{66})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 840 q - 16 q^{3} - 126 q^{4} - 25 q^{6} - 34 q^{7} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 840 q - 16 q^{3} - 126 q^{4} - 25 q^{6} - 34 q^{7} - 24 q^{9} - 50 q^{10} + 168 q^{12} - 38 q^{13} - 100 q^{15} + 86 q^{16} - 33 q^{18} - 6 q^{19} - 118 q^{21} + 256 q^{22} + 170 q^{24} + 384 q^{25} - 160 q^{27} - 652 q^{28} - 40 q^{30} + 72 q^{31} - 113 q^{33} + 10 q^{34} - 127 q^{36} + 2 q^{37} - 51 q^{39} - 172 q^{40} - 274 q^{42} + 50 q^{43} - 518 q^{45} + 1070 q^{46} + 281 q^{48} + 132 q^{49} - 37 q^{51} - 2024 q^{52} - 809 q^{54} - 1810 q^{55} + 546 q^{57} - 716 q^{58} - 2 q^{60} + 410 q^{61} + 1371 q^{63} - 144 q^{64} - 814 q^{66} + 460 q^{67} - 123 q^{69} - 1296 q^{70} + 1196 q^{72} + 1324 q^{73} + 208 q^{75} + 1588 q^{76} - 118 q^{78} + 66 q^{79} + 220 q^{81} + 2412 q^{82} - 2123 q^{84} + 50 q^{85} - 954 q^{87} - 14 q^{88} - 504 q^{90} - 36 q^{91} - 1271 q^{93} - 1328 q^{94} + 1335 q^{96} - 90 q^{97} - 16 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 −0.372771 − 3.90383i −0.867999 − 2.87169i −11.1732 + 2.15346i 2.04976 + 0.294710i −10.8870 + 4.45900i −4.95140 − 6.95327i 8.15244 + 27.7647i −7.49316 + 4.98524i 0.386411 − 8.11176i
17.2 −0.365428 − 3.82693i 2.09890 + 2.14350i −10.5841 + 2.03993i −7.82250 − 1.12471i 7.43604 − 8.81565i 5.16070 + 7.24719i 7.34209 + 25.0049i −0.189206 + 8.99801i −1.44561 + 30.3472i
17.3 −0.339674 − 3.55723i −2.79427 + 1.09181i −8.61080 + 1.65960i 4.72450 + 0.679280i 4.83296 + 9.56901i 4.33674 + 6.09010i 4.80145 + 16.3522i 6.61591 − 6.10162i 0.811566 − 17.0369i
17.4 −0.316674 − 3.31636i 2.98394 + 0.310028i −6.97027 + 1.34341i 4.38305 + 0.630187i 0.0832287 − 9.99400i −3.34678 − 4.69989i 2.90823 + 9.90451i 8.80777 + 1.85021i 0.701931 − 14.7353i
17.5 −0.315296 − 3.30193i −0.380346 + 2.97579i −6.87561 + 1.32517i 1.00410 + 0.144367i 9.94578 + 0.317620i −4.51680 − 6.34296i 2.80549 + 9.55461i −8.71067 − 2.26366i 0.160103 − 3.36097i
17.6 −0.300568 − 3.14769i −2.02846 − 2.21028i −5.88990 + 1.13519i −3.30027 − 0.474508i −6.34760 + 7.04931i 7.22926 + 10.1521i 1.78017 + 6.06270i −0.770704 + 8.96694i −0.501647 + 10.5309i
17.7 −0.287750 − 3.01346i 2.06232 − 2.17873i −5.07042 + 0.977244i −5.16381 − 0.742444i −7.15894 − 5.58777i −0.342776 − 0.481361i 0.992495 + 3.38013i −0.493707 − 8.98645i −0.751435 + 15.7746i
17.8 −0.258098 − 2.70292i 1.18857 − 2.75451i −3.31147 + 0.638234i 8.17030 + 1.17471i −7.75199 − 2.50167i 5.28772 + 7.42556i −0.480079 − 1.63500i −6.17462 − 6.54783i 1.06642 − 22.3869i
17.9 −0.253296 − 2.65263i −2.66207 − 1.38324i −3.04458 + 0.586794i −6.58359 − 0.946578i −2.99494 + 7.41187i −3.47491 − 4.87983i −0.675202 − 2.29953i 5.17328 + 7.36459i −0.843327 + 17.7036i
17.10 −0.238781 − 2.50063i 2.20075 + 2.03880i −2.26841 + 0.437200i 4.46322 + 0.641713i 4.57279 − 5.99007i 5.28893 + 7.42726i −1.19593 − 4.07295i 0.686561 + 8.97377i 0.538955 − 11.3141i
17.11 −0.223275 − 2.33824i −1.10838 + 2.78774i −1.48980 + 0.287135i −3.05677 − 0.439497i 6.76587 + 1.96923i 2.18219 + 3.06445i −1.64299 − 5.59553i −6.54298 − 6.17976i −0.345149 + 7.24558i
17.12 −0.217915 − 2.28210i −2.97742 − 0.367411i −1.23280 + 0.237603i 5.68528 + 0.817420i −0.189647 + 6.87484i −3.86064 − 5.42151i −1.77259 − 6.03689i 8.73002 + 2.18787i 0.626532 − 13.1525i
17.13 −0.155968 − 1.63338i 2.15774 + 2.08427i 1.28412 − 0.247495i −9.24803 − 1.32967i 3.06785 − 3.84948i −6.62008 − 9.29660i −2.45361 − 8.35622i 0.311677 + 8.99460i −0.729443 + 15.3129i
17.14 −0.152393 − 1.59594i 0.135358 − 2.99694i 1.40393 − 0.270585i 0.199274 + 0.0286513i −4.80356 + 0.240692i −2.27333 − 3.19244i −2.45247 − 8.35236i −8.96336 − 0.811320i 0.0153576 − 0.322395i
17.15 −0.132486 − 1.38746i −2.67554 + 1.35701i 2.02022 − 0.389366i −4.99218 − 0.717767i 2.23728 + 3.53242i 1.84316 + 2.58836i −2.37856 − 8.10065i 5.31703 − 7.26149i −0.334478 + 7.02155i
17.16 −0.127499 − 1.33522i 1.42593 + 2.63945i 2.16114 − 0.416527i 5.12044 + 0.736208i 3.34246 − 2.24047i −4.38585 − 6.15907i −2.34325 − 7.98037i −4.93343 + 7.52737i 0.330155 − 6.93081i
17.17 −0.105003 − 1.09964i 2.99034 − 0.240568i 2.72952 − 0.526072i −2.36755 − 0.340403i −0.578535 − 3.26305i 3.93452 + 5.52527i −2.10996 − 7.18587i 8.88425 − 1.43876i −0.125721 + 2.63921i
17.18 −0.0816192 − 0.854754i 2.61588 − 1.46873i 3.20377 − 0.617476i 6.65997 + 0.957559i −1.46891 − 2.11606i −5.73553 − 8.05442i −1.75691 − 5.98349i 4.68569 − 7.68403i 0.274897 − 5.77079i
17.19 −0.0720449 − 0.754488i −0.695849 − 2.91818i 3.36365 − 0.648291i −3.62054 − 0.520555i −2.15160 + 0.735250i −1.07696 − 1.51238i −1.58559 − 5.40001i −8.03159 + 4.06123i −0.131911 + 2.76916i
17.20 −0.0661166 − 0.692405i −0.991594 + 2.83139i 3.45266 − 0.665446i 8.44666 + 1.21445i 2.02602 + 0.499383i 3.65289 + 5.12977i −1.47288 − 5.01616i −7.03348 − 5.61517i 0.282424 − 5.92880i
See next 80 embeddings (of 840 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 17.42
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
67.g even 33 1 inner
201.o odd 66 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 201.3.o.b ✓ 840
3.b odd 2 1 inner 201.3.o.b ✓ 840
67.g even 33 1 inner 201.3.o.b ✓ 840
201.o odd 66 1 inner 201.3.o.b ✓ 840
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
201.3.o.b ✓ 840 1.a even 1 1 trivial
201.3.o.b ✓ 840 3.b odd 2 1 inner
201.3.o.b ✓ 840 67.g even 33 1 inner
201.3.o.b ✓ 840 201.o odd 66 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{840} + 147 T_{2}^{838} + 10201 T_{2}^{836} + 432034 T_{2}^{834} + 11800987 T_{2}^{832} + \cdots + 10\!\cdots\!96 \) acting on \(S_{3}^{\mathrm{new}}(201, [\chi])\). Copy content Toggle raw display