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Properties

Label 95.11.n.a
Level $95$
Weight $11$
Character orbit 95.n
Analytic conductor $60.359$
Analytic rank $0$
Dimension $396$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,11,Mod(21,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.21");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 95.n (of order \(18\), degree \(6\), 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: \(60.3589390040\)
Analytic rank: \(0\)
Dimension: \(396\)
Relative dimension: \(66\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 396 q + 132 q^{3} - 1830 q^{4} + 3066 q^{6} - 95436 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 396 q + 132 q^{3} - 1830 q^{4} + 3066 q^{6} - 95436 q^{9} - 93750 q^{10} + 2985984 q^{12} - 2110026 q^{13} + 1224960 q^{14} - 6809430 q^{16} + 532380 q^{17} - 7959948 q^{19} - 9580518 q^{21} - 31211136 q^{22} - 13532700 q^{23} + 21417984 q^{24} - 159720 q^{26} - 183408156 q^{27} + 144654336 q^{28} - 140983194 q^{29} - 119625000 q^{30} + 122776776 q^{31} + 393148500 q^{32} - 359004150 q^{33} - 578370492 q^{34} - 59812500 q^{35} - 640932912 q^{36} + 503327622 q^{38} + 1302975096 q^{39} - 96000000 q^{40} - 1194423528 q^{41} - 3390185778 q^{42} - 670104582 q^{43} + 2150443914 q^{44} + 3016431090 q^{46} - 151507770 q^{47} + 364629606 q^{48} - 8225668806 q^{49} + 3009006312 q^{51} - 2363609406 q^{52} - 4515798744 q^{53} - 9311985042 q^{54} + 952636938 q^{57} + 4039140864 q^{58} + 5041664862 q^{59} - 2779312500 q^{60} + 5128963260 q^{61} - 4033454760 q^{62} - 12114094326 q^{63} + 11990621196 q^{64} - 3916687500 q^{65} - 1806217476 q^{66} + 6379678362 q^{67} + 18479546670 q^{68} + 14567082498 q^{69} - 1621125000 q^{70} - 1788156144 q^{71} - 16923552852 q^{72} - 26786299530 q^{73} + 15012453948 q^{74} + 18346685868 q^{76} + 6003303804 q^{77} + 69668310660 q^{78} - 9538312266 q^{79} + 5565750000 q^{80} + 2012656020 q^{81} + 30701977302 q^{82} - 21873008760 q^{83} - 51655671540 q^{84} - 14398500000 q^{85} - 14081837694 q^{86} - 17926323216 q^{87} + 110136441168 q^{88} + 77332013844 q^{89} + 18945093750 q^{90} - 85587979728 q^{91} + 50548839756 q^{92} - 13898204208 q^{93} + 262589518236 q^{96} + 29548158042 q^{97} - 235808629536 q^{98} - 91369111794 q^{99}+O(q^{100}) \) 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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
21.1 −61.1091 − 10.7752i 90.6903 − 108.081i 2655.97 + 966.695i −1313.26 + 477.988i −6706.59 + 5627.50i 1391.50 + 2410.15i −96859.5 − 55921.9i 6797.09 + 38548.2i 85402.6 − 15058.8i
21.2 −59.5178 − 10.4946i −238.205 + 283.882i 2469.99 + 899.002i 1313.26 − 477.988i 17156.7 − 14396.1i 3332.39 + 5771.87i −83978.3 − 48484.9i −13593.4 − 77092.1i −83178.7 + 14666.6i
21.3 −57.7744 − 10.1872i 6.52713 − 7.77873i 2271.86 + 826.889i 1313.26 − 477.988i −456.345 + 382.919i −4938.84 − 8554.32i −70806.3 − 40880.1i 10235.8 + 58050.4i −80742.2 + 14237.0i
21.4 −57.3380 − 10.1102i −246.025 + 293.202i 2223.18 + 809.171i −1313.26 + 477.988i 17070.9 − 14324.2i −3262.03 − 5650.01i −67659.4 − 39063.2i −15185.0 − 86118.3i 80132.2 − 14129.5i
21.5 −56.2513 − 9.91861i 283.038 − 337.311i 2103.58 + 765.641i 1313.26 − 477.988i −19266.9 + 16166.8i −8601.00 − 14897.4i −60081.2 − 34687.9i −23414.7 − 132791.i −78613.5 + 13861.7i
21.6 −55.8946 − 9.85573i −94.5815 + 112.718i 2064.83 + 751.535i −1313.26 + 477.988i 6397.51 − 5368.15i 7163.28 + 12407.2i −57673.1 − 33297.6i 6494.10 + 36829.9i 78115.1 − 13773.8i
21.7 −51.6407 − 9.10564i 231.862 − 276.323i 1621.60 + 590.214i −1313.26 + 477.988i −14489.6 + 12158.2i −4425.19 − 7664.65i −31864.3 − 18396.9i −12340.4 − 69985.7i 72170.0 − 12725.5i
21.8 −50.8093 − 8.95904i −106.608 + 127.051i 1539.07 + 560.176i 1313.26 − 477.988i 6554.95 − 5500.26i 12381.7 + 21445.8i −27427.2 − 15835.1i 5477.15 + 31062.5i −71008.1 + 12520.6i
21.9 −49.0540 − 8.64954i 84.6169 − 100.843i 1369.23 + 498.360i −1313.26 + 477.988i −5023.04 + 4214.83i −12628.7 − 21873.6i −18683.1 − 10786.7i 7244.56 + 41085.9i 68555.0 − 12088.1i
21.10 −47.5593 − 8.38598i 230.589 − 274.806i 1229.31 + 447.434i −1313.26 + 477.988i −13271.2 + 11135.8i 14205.4 + 24604.4i −11886.4 − 6862.64i −12093.0 − 68582.6i 66466.1 − 11719.8i
21.11 −45.6687 − 8.05262i 180.078 − 214.608i 1058.54 + 385.276i 1313.26 − 477.988i −9952.08 + 8350.78i 14827.6 + 25682.2i −4115.32 − 2375.98i −3374.99 − 19140.5i −63823.9 + 11253.9i
21.12 −44.4252 − 7.83336i 52.7241 − 62.8342i 949.993 + 345.769i 1313.26 − 477.988i −2834.48 + 2378.41i −3796.41 − 6575.58i 509.392 + 294.098i 9085.45 + 51526.2i −62086.1 + 10947.5i
21.13 −42.7196 − 7.53262i 216.249 − 257.716i 805.978 + 293.352i 1313.26 − 477.988i −11179.3 + 9380.59i 1612.29 + 2792.57i 6247.25 + 3606.85i −9399.94 − 53309.7i −59702.4 + 10527.2i
21.14 −42.3555 − 7.46841i −264.359 + 315.050i 775.963 + 282.427i −1313.26 + 477.988i 13550.0 − 11369.8i −2364.23 − 4094.96i 7383.72 + 4262.99i −19117.5 − 108421.i 59193.6 − 10437.4i
21.15 −40.9201 − 7.21531i −230.168 + 274.304i 660.147 + 240.274i 1313.26 − 477.988i 11397.7 − 9563.80i −2238.39 − 3877.00i 11568.5 + 6679.10i −12011.4 − 68120.1i −57187.5 + 10083.7i
21.16 −40.1539 − 7.08022i −57.0549 + 67.9954i 599.962 + 218.368i −1313.26 + 477.988i 2772.40 − 2326.32i 3046.11 + 5276.02i 13613.5 + 7859.76i 8885.64 + 50393.0i 56116.8 − 9894.90i
21.17 −37.5879 − 6.62777i −167.186 + 199.244i 406.681 + 148.020i 1313.26 − 477.988i 7604.72 − 6381.11i −12140.7 − 21028.2i 19542.3 + 11282.8i −1493.44 − 8469.71i −52530.8 + 9262.59i
21.18 −30.0368 − 5.29630i 85.7905 − 102.241i −88.0867 − 32.0609i −1313.26 + 477.988i −3118.37 + 2616.63i −360.285 − 624.031i 29523.9 + 17045.6i 7160.51 + 40609.3i 41977.7 − 7401.80i
21.19 −27.5211 − 4.85272i −183.416 + 218.587i −228.382 − 83.1241i −1313.26 + 477.988i 6108.56 − 5125.69i −4255.32 − 7370.44i 30664.5 + 17704.1i −3884.98 − 22032.8i 38461.9 − 6781.88i
21.20 −23.9059 − 4.21526i 25.9976 − 30.9827i −408.520 − 148.689i 1313.26 − 477.988i −752.096 + 631.084i 8280.45 + 14342.2i 30666.4 + 17705.2i 9969.70 + 56541.0i −33409.6 + 5891.01i
See next 80 embeddings (of 396 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 21.66
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.f odd 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.11.n.a ✓ 396
19.f odd 18 1 inner 95.11.n.a ✓ 396
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.11.n.a ✓ 396 1.a even 1 1 trivial
95.11.n.a ✓ 396 19.f odd 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{11}^{\mathrm{new}}(95, [\chi])\).