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Properties

Label 23.11.d.a
Level $23$
Weight $11$
Character orbit 23.d
Analytic conductor $14.613$
Analytic rank $0$
Dimension $190$
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] = [23,11,Mod(5,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.5");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 23.d (of order \(22\), degree \(10\), 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: \(14.6132168115\)
Analytic rank: \(0\)
Dimension: \(190\)
Relative dimension: \(19\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9} - 11 q^{10} - 11 q^{11} - 311414 q^{12} + 615881 q^{13} - 11 q^{14} - 4830144 q^{15} + 4888037 q^{16} + 1092014 q^{17} - 12368454 q^{18} - 2415644 q^{19} + 25028597 q^{20} + 26277196 q^{21} - 27677088 q^{23} - 86512102 q^{24} + 27883308 q^{25} + 19713282 q^{26} + 71519392 q^{27} + 43862005 q^{28} + 14189630 q^{29} - 270003723 q^{30} - 143915692 q^{31} + 282266229 q^{32} - 54918402 q^{33} - 124580401 q^{34} - 190738351 q^{35} + 455227393 q^{36} + 518658261 q^{37} - 208458646 q^{38} - 527477093 q^{39} - 1236125011 q^{40} + 306361793 q^{41} + 1644990919 q^{42} + 997299501 q^{43} + 1314948338 q^{44} - 983375619 q^{46} - 1197840554 q^{47} - 3164309566 q^{48} + 634842426 q^{49} - 1020294456 q^{50} + 2177981773 q^{51} + 7146448896 q^{52} + 679896965 q^{53} - 2477743998 q^{54} - 7228070785 q^{55} - 4503370696 q^{56} + 2289855898 q^{57} + 6681134963 q^{58} + 3429280247 q^{59} - 14840793781 q^{60} - 5311011871 q^{61} - 2481918590 q^{62} - 453734886 q^{63} + 9411259010 q^{64} + 10772645950 q^{65} + 12902167608 q^{66} + 2086349727 q^{67} - 722851896 q^{69} - 14032163318 q^{70} - 9791640554 q^{71} - 17117854769 q^{72} - 3808899929 q^{73} + 28336591052 q^{74} + 11315752564 q^{75} + 3533940894 q^{76} + 10258348964 q^{77} + 32629640016 q^{78} + 11295172361 q^{79} - 32343151082 q^{80} - 59771908210 q^{81} - 19730142428 q^{82} - 14758669948 q^{83} + 3906513611 q^{84} - 18216984945 q^{85} - 6838112941 q^{86} + 33011018419 q^{87} + 50131567101 q^{88} + 34310737417 q^{89} + 65550641882 q^{90} - 21333991814 q^{92} - 60352716136 q^{93} - 23758977011 q^{94} - 40681791604 q^{95} - 193570603643 q^{96} - 50355692024 q^{97} + 86096143637 q^{98} + 177617674300 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1 −56.2787 − 16.5249i 234.062 − 270.123i 2032.78 + 1306.39i −3980.54 − 572.315i −17636.5 + 11334.3i 21107.4 − 9639.44i −53481.6 − 61721.0i −9777.37 − 68003.1i 214562. + 97987.1i
5.2 −55.1016 − 16.1793i −267.468 + 308.675i 1912.97 + 1229.39i −1056.35 − 151.880i 19732.1 − 12681.0i −3001.68 + 1370.82i −47007.4 − 54249.4i −15337.3 − 106673.i 55749.3 + 25459.9i
5.3 −54.0162 − 15.8606i 50.7421 − 58.5595i 1804.75 + 1159.84i 5412.82 + 778.246i −3669.68 + 2358.36i −4757.37 + 2172.62i −41338.8 − 47707.5i 7549.10 + 52505.1i −280037. − 127888.i
5.4 −41.5173 − 12.1906i −25.3274 + 29.2294i 713.629 + 458.622i −2142.16 − 307.996i 1407.85 − 904.770i −6037.55 + 2757.26i 4978.81 + 5745.85i 8190.67 + 56967.4i 85182.1 + 38901.3i
5.5 −28.3423 − 8.32206i 256.272 − 295.754i −127.412 − 81.8829i −273.245 − 39.2867i −9724.64 + 6249.65i −23766.3 + 10853.7i 22737.8 + 26240.8i −13391.4 − 93139.2i 7417.46 + 3387.44i
5.6 −25.2998 − 7.42869i −190.721 + 220.104i −276.549 − 177.727i 1790.89 + 257.491i 6460.29 − 4151.78i 15874.6 − 7249.67i 23358.1 + 26956.6i −3667.63 − 25508.9i −43396.3 − 19818.4i
5.7 −24.8561 − 7.29842i 190.277 − 219.591i −296.883 − 190.795i 3173.14 + 456.228i −6332.21 + 4069.47i 23554.6 − 10757.0i 23358.5 + 26957.1i −3611.46 − 25118.2i −75542.2 − 34499.0i
5.8 −7.05466 − 2.07144i 17.6962 − 20.4225i −815.966 − 524.390i −5359.18 − 770.533i −167.144 + 107.417i 10779.3 − 4922.74i 9600.54 + 11079.6i 8299.63 + 57725.2i 36211.1 + 16537.0i
5.9 −6.99589 − 2.05418i −112.150 + 129.428i −816.721 − 524.875i 4457.99 + 640.963i 1050.46 − 675.088i −27977.7 + 12777.0i 9524.84 + 10992.3i 4229.56 + 29417.3i −29871.0 − 13641.6i
5.10 −0.740659 − 0.217477i −295.459 + 340.978i −860.942 − 553.294i −3454.08 − 496.622i 292.990 − 188.293i −17524.4 + 8003.14i 1034.97 + 1194.42i −20566.4 − 143043.i 2450.29 + 1119.01i
5.11 7.54558 + 2.21558i 84.3433 − 97.3374i −809.417 − 520.181i −216.245 − 31.0913i 852.078 − 547.597i −8814.57 + 4025.48i −10228.5 − 11804.3i 6042.78 + 42028.4i −1562.81 − 713.709i
5.12 13.2778 + 3.89872i 182.294 − 210.378i −700.343 − 450.083i 1698.06 + 244.144i 3240.67 − 2082.65i 9755.84 − 4455.34i −16824.0 − 19415.9i −2624.45 − 18253.5i 21594.7 + 9861.95i
5.13 25.4271 + 7.46607i −119.335 + 137.720i −270.648 − 173.935i 4505.25 + 647.757i −4062.57 + 2610.86i 11932.1 − 5449.19i −23353.9 − 26951.8i 3677.61 + 25578.3i 109719. + 50107.1i
5.14 30.3985 + 8.92579i −183.914 + 212.248i −17.0475 − 10.9558i −1508.74 − 216.924i −7485.18 + 4810.43i 12346.2 − 5638.33i −21665.5 − 25003.3i −2821.33 − 19622.8i −43927.2 − 20060.9i
5.15 32.9159 + 9.66497i 294.618 − 340.007i 128.599 + 82.6457i −4739.48 − 681.434i 12983.8 − 8344.16i −428.091 + 195.502i −19570.3 − 22585.3i −20401.6 − 141896.i −149418. − 68237.0i
5.16 43.9370 + 12.9011i −46.3131 + 53.4482i 902.580 + 580.053i −2494.45 − 358.647i −2724.40 + 1750.87i −21084.8 + 9629.08i 1466.36 + 1692.27i 7691.74 + 53497.3i −104972. − 47938.9i
5.17 47.0781 + 13.8234i 169.037 − 195.079i 1163.81 + 747.938i 3647.86 + 524.483i 10654.6 − 6847.29i −5261.26 + 2402.74i 11548.9 + 13328.1i −1078.80 − 7503.20i 164484. + 75117.3i
5.18 57.4680 + 16.8741i 42.8012 − 49.3952i 2156.39 + 1385.83i −2527.86 − 363.452i 3293.20 − 2116.41i 28411.7 − 12975.2i 60375.3 + 69676.8i 7795.60 + 54219.6i −139138. − 63542.4i
5.19 58.0720 + 17.0515i −299.179 + 345.271i 2220.16 + 1426.81i 3804.62 + 547.022i −23261.3 + 14949.1i −11603.6 + 5299.20i 64014.2 + 73876.3i −21300.4 − 148148.i 211615. + 96641.2i
7.1 −40.8007 + 47.0865i −166.294 + 106.871i −406.713 − 2828.75i −2779.67 + 1269.43i 1752.75 − 12190.6i −4308.90 − 14674.8i 96118.5 + 61771.6i −8297.48 + 18168.9i 53639.3 − 182679.i
See next 80 embeddings (of 190 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5.19
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.d odd 22 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 23.11.d.a ✓ 190
23.d odd 22 1 inner 23.11.d.a ✓ 190
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
23.11.d.a ✓ 190 1.a even 1 1 trivial
23.11.d.a ✓ 190 23.d odd 22 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{11}^{\mathrm{new}}(23, [\chi])\).