Properties

Label 23.10.c.a
Level $23$
Weight $10$
Character orbit 23.c
Analytic conductor $11.846$
Analytic rank $0$
Dimension $170$
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] = [23,10,Mod(2,23)]
 
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([2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 23.c (of order \(11\), 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: \(11.8458242318\)
Analytic rank: \(0\)
Dimension: \(170\)
Relative dimension: \(17\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 170 q - 43 q^{2} - 157 q^{3} - 4619 q^{4} + 2265 q^{5} + 1532 q^{6} + 8605 q^{7} - 28412 q^{8} - 84756 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 170 q - 43 q^{2} - 157 q^{3} - 4619 q^{4} + 2265 q^{5} + 1532 q^{6} + 8605 q^{7} - 28412 q^{8} - 84756 q^{9} - 1485 q^{10} + 81163 q^{11} - 60588 q^{12} - 11089 q^{13} + 67821 q^{14} + 621703 q^{15} - 1909531 q^{16} - 753661 q^{17} - 726672 q^{18} + 2352257 q^{19} + 6591465 q^{20} - 5684355 q^{21} - 5946642 q^{22} - 4490346 q^{23} + 4177174 q^{24} + 545458 q^{25} + 10422936 q^{26} - 1144735 q^{27} - 5527093 q^{28} - 7002529 q^{29} - 24506121 q^{30} + 11263929 q^{31} + 46016973 q^{32} - 1003951 q^{33} - 12993751 q^{34} + 68486143 q^{35} - 39331073 q^{36} - 89526363 q^{37} - 94102532 q^{38} + 49805983 q^{39} + 272326679 q^{40} + 52330165 q^{41} + 66250835 q^{42} - 21814465 q^{43} - 105726610 q^{44} - 198216616 q^{45} - 320080243 q^{46} - 153217032 q^{47} + 325997510 q^{48} + 195154842 q^{49} + 365787994 q^{50} + 174282061 q^{51} - 10096756 q^{52} - 224456041 q^{53} - 1140098178 q^{54} - 379496843 q^{55} + 389457460 q^{56} + 84964017 q^{57} + 547323529 q^{58} + 129076539 q^{59} - 1362120205 q^{60} + 447029913 q^{61} + 796216240 q^{62} + 1061159027 q^{63} + 922158762 q^{64} - 180608527 q^{65} + 277416862 q^{66} - 319825461 q^{67} - 2693182722 q^{68} - 1160581515 q^{69} - 452062394 q^{70} + 97280089 q^{71} + 437472589 q^{72} + 839365275 q^{73} + 1826280178 q^{74} + 2985570317 q^{75} + 6472764418 q^{76} - 338423227 q^{77} - 4686899840 q^{78} - 4912832511 q^{79} - 7619127772 q^{80} - 5223670776 q^{81} + 1981501322 q^{82} + 806964537 q^{83} + 10896222429 q^{84} + 6493376823 q^{85} + 1571113345 q^{86} + 3874701515 q^{87} - 1784251567 q^{88} - 1388933039 q^{89} - 7300929742 q^{90} - 3850658378 q^{91} - 6763730354 q^{92} - 4102556922 q^{93} + 62806987 q^{94} - 5662987785 q^{95} + 19038690045 q^{96} + 10282527577 q^{97} + 6376122113 q^{98} + 11619425557 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −37.2704 23.9522i 17.9475 + 124.827i 602.681 + 1319.69i 1413.32 + 414.989i 2320.98 5082.24i −7622.70 + 8797.06i 5919.11 41168.3i 3625.96 1064.68i −42735.1 49319.0i
2.2 −31.7148 20.3818i −5.04104 35.0612i 377.715 + 827.080i −472.249 138.665i −554.737 + 1214.70i 7160.89 8264.11i 2131.30 14823.5i 17681.8 5191.85i 12151.0 + 14023.0i
2.3 −26.6551 17.1302i −29.0863 202.300i 204.359 + 447.484i 210.621 + 61.8440i −2690.14 + 5890.58i −3087.20 + 3562.81i −90.4594 + 629.159i −21193.5 + 6222.98i −4554.74 5256.45i
2.4 −23.7212 15.2447i 20.3997 + 141.883i 117.602 + 257.513i −2176.95 639.211i 1679.06 3676.62i −2868.99 + 3310.99i −918.575 + 6388.83i −828.913 + 243.391i 41895.4 + 48349.8i
2.5 −19.3117 12.4109i 32.9551 + 229.208i 6.22000 + 13.6199i 1344.48 + 394.774i 2208.25 4835.40i 4195.31 4841.65i −1623.77 + 11293.6i −32564.4 + 9561.77i −21064.7 24309.9i
2.6 −14.3223 9.20438i −1.55598 10.8221i −92.2849 202.076i 1543.83 + 453.310i −77.3256 + 169.319i −1288.91 + 1487.48i −1778.78 + 12371.7i 18771.0 5511.66i −17938.8 20702.5i
2.7 −5.08899 3.27050i −22.3597 155.515i −197.491 432.445i −2066.95 606.911i −394.824 + 864.544i 137.421 158.592i −850.062 + 5912.31i −4799.38 + 1409.22i 8533.78 + 9848.51i
2.8 −3.75865 2.41553i 3.02788 + 21.0594i −204.400 447.573i −84.8947 24.9273i 39.4889 86.4687i −1251.63 + 1444.46i −638.417 + 4440.29i 18451.4 5417.81i 258.876 + 298.759i
2.9 2.27840 + 1.46424i −34.9692 243.216i −209.645 459.059i 1977.74 + 580.717i 276.452 605.346i 7648.62 8826.98i 391.860 2725.44i −39045.5 + 11464.8i 3655.77 + 4218.98i
2.10 7.63720 + 4.90813i 33.3373 + 231.866i −178.455 390.763i −458.130 134.519i −883.424 + 1934.43i −5366.11 + 6192.82i 1216.51 8461.03i −33764.7 + 9914.20i −2838.60 3275.91i
2.11 8.38475 + 5.38855i 19.8184 + 137.840i −171.425 375.368i −910.049 267.214i −576.587 + 1262.55i 6824.79 7876.23i 1311.58 9122.25i 278.549 81.7895i −6190.63 7144.37i
2.12 15.2974 + 9.83105i −1.23691 8.60291i −75.3311 164.952i 1465.21 + 430.225i 65.6541 143.762i −3094.73 + 3571.51i 1794.27 12479.4i 18813.2 5524.06i 18184.4 + 20985.9i
2.13 19.2422 + 12.3662i −28.9842 201.590i 4.64721 + 10.1760i −323.193 94.8980i 1935.18 4237.46i −6396.47 + 7381.92i 1630.25 11338.6i −20912.7 + 6140.52i −5045.42 5822.73i
2.14 24.1470 + 15.5184i −11.1258 77.3816i 129.568 + 283.713i −1221.63 358.703i 932.181 2041.19i 4026.47 4646.80i 817.403 5685.16i 13021.6 3823.48i −23932.3 27619.3i
2.15 27.3293 + 17.5635i 24.5672 + 170.869i 225.721 + 494.261i 2459.29 + 722.112i −2329.64 + 5101.20i 3138.36 3621.86i −145.002 + 1008.51i −9706.90 + 2850.20i 54527.7 + 62928.3i
2.16 32.1827 + 20.6826i 19.4420 + 135.222i 395.267 + 865.514i −1263.96 371.131i −2171.05 + 4753.93i −2843.93 + 3282.07i −2392.79 + 16642.2i 978.645 287.356i −33001.6 38085.9i
2.17 35.8106 + 23.0141i −23.3833 162.634i 540.060 + 1182.57i 1123.63 + 329.927i 2905.51 6362.18i 1437.36 1658.80i −4774.07 + 33204.4i −7017.38 + 2060.49i 32644.8 + 37674.1i
3.1 −5.68739 39.5567i −6.59512 + 14.4413i −1041.12 + 305.701i −439.442 + 507.143i 608.758 + 178.748i 370.747 238.264i 9513.86 + 20832.5i 12724.6 + 14684.9i 22560.2 + 14498.5i
3.2 −5.05902 35.1863i 93.0827 203.823i −721.220 + 211.769i 966.721 1115.66i −7642.67 2244.09i −2470.85 + 1587.92i 3539.23 + 7749.84i −19989.7 23069.4i −44146.4 28371.2i
3.3 −4.42307 30.7631i −74.9596 + 164.139i −435.545 + 127.888i 1553.11 1792.39i 5380.97 + 1579.99i −2794.08 + 1795.65i −749.704 1641.62i −8432.94 9732.14i −62008.9 39850.7i
See next 80 embeddings (of 170 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.17
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 23.10.c.a 170
23.c even 11 1 inner 23.10.c.a 170
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
23.10.c.a 170 1.a even 1 1 trivial
23.10.c.a 170 23.c even 11 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{10}^{\mathrm{new}}(23, [\chi])\).