Properties

Label 11.15.d.a
Level $11$
Weight $15$
Character orbit 11.d
Analytic conductor $13.676$
Analytic rank $0$
Dimension $52$
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] = [11,15,Mod(2,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.2");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 11.d (of order \(10\), degree \(4\), 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: \(13.6761864967\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(13\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 52 q - 5 q^{2} + 3312 q^{3} + 114135 q^{4} + 34876 q^{5} + 715515 q^{6} + 1575010 q^{7} - 7454725 q^{8} - 3174071 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 52 q - 5 q^{2} + 3312 q^{3} + 114135 q^{4} + 34876 q^{5} + 715515 q^{6} + 1575010 q^{7} - 7454725 q^{8} - 3174071 q^{9} - 3655827 q^{11} + 94765698 q^{12} + 26095660 q^{13} - 603550398 q^{14} - 5980560 q^{15} + 582219319 q^{16} - 117898480 q^{17} - 1464783390 q^{18} - 312644675 q^{19} + 2471518904 q^{20} - 13735692995 q^{22} - 18616322228 q^{23} + 45239874305 q^{24} - 12236967411 q^{25} + 9881999442 q^{26} + 21359571891 q^{27} - 8113875060 q^{28} - 448248840 q^{29} - 46588729580 q^{30} + 16239668846 q^{31} - 99959209483 q^{33} + 4892182882 q^{34} - 121969992120 q^{35} + 891977487638 q^{36} + 254149476378 q^{37} - 236105595100 q^{38} - 1271591675590 q^{39} - 32771062860 q^{40} + 1388348160280 q^{41} - 112593364810 q^{42} - 3456841408436 q^{44} - 1233179241624 q^{45} + 845675977710 q^{46} + 1158693582258 q^{47} + 5047096511312 q^{48} + 2775659539775 q^{49} - 5396000841345 q^{50} - 3863898507855 q^{51} + 5309769987710 q^{52} + 4456015847472 q^{53} - 16652309857996 q^{55} - 10310995614876 q^{56} + 18601573122465 q^{57} + 5013537545020 q^{58} + 2792530662811 q^{59} + 3433084089440 q^{60} - 11116738289030 q^{61} + 9108734500320 q^{62} + 16954172197290 q^{63} + 5433572912647 q^{64} - 19406705677170 q^{66} - 13742744314622 q^{67} - 40163255299800 q^{68} + 22682824281182 q^{69} + 17475348332780 q^{70} - 32319550303036 q^{71} + 49433858016325 q^{72} + 49225398585780 q^{73} - 115659431324650 q^{74} - 44698263856095 q^{75} + 138804615410800 q^{77} + 90318383509960 q^{78} - 1708076734610 q^{79} - 179216833922324 q^{80} - 142379206199180 q^{81} + 83960277644305 q^{82} + 26463988076165 q^{83} + 56454093682650 q^{84} + 26992332006260 q^{85} + 23877679248947 q^{86} + 230715306801595 q^{88} - 155234952718542 q^{89} - 20038022006720 q^{90} - 170611600181648 q^{91} - 374911327331192 q^{92} + 240520199236144 q^{93} + 543279860205720 q^{94} + 181639455148500 q^{95} - 56860816268540 q^{96} - 275471492938977 q^{97} + 201401388195115 q^{99}+O(q^{100}) \) 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 −236.091 76.7107i 1404.04 1020.09i 36599.6 + 26591.2i 17129.5 + 52719.2i −409733. + 133130.i 347419. 478181.i −4.21038e6 5.79510e6i −547289. + 1.68438e6i 1.37606e7i
2.2 −199.758 64.9052i −3456.81 + 2511.52i 22435.6 + 16300.4i −9471.22 29149.4i 853535. 277330.i −55107.8 + 75849.3i −1.40098e6 1.92828e6i 4.16378e6 1.28148e7i 6.43755e6i
2.3 −157.861 51.2920i 79.9689 58.1008i 9034.19 + 6563.72i −14721.0 45306.7i −15604.0 + 5070.06i −565560. + 778426.i 509000. + 700579.i −1.47500e6 + 4.53958e6i 7.90722e6i
2.4 −119.417 38.8010i 3112.87 2261.63i −499.976 363.254i −39265.4 120847.i −459484. + 149295.i 577116. 794332.i 1.25481e6 + 1.72710e6i 3.09696e6 9.53146e6i 1.59547e7i
2.5 −116.568 37.8754i −829.952 + 602.996i −1101.28 800.129i 25059.8 + 77126.2i 119585. 38855.5i 411520. 566408.i 1.27843e6 + 1.75960e6i −1.15280e6 + 3.54796e6i 9.93962e6i
2.6 −57.1439 18.5672i 2553.58 1855.29i −10334.3 7508.27i 43338.6 + 133382.i −180369. + 58605.5i −281229. + 387078.i 1.02976e6 + 1.41735e6i 1.60068e6 4.92639e6i 8.42667e6i
2.7 −13.9048 4.51795i −1467.63 + 1066.30i −13082.0 9504.63i −19976.8 61482.1i 25224.6 8195.98i 351170. 483344.i 279760. + 385057.i −461067. + 1.41902e6i 945153.i
2.8 47.9694 + 15.5862i −2902.88 + 2109.07i −11196.8 8134.95i 33214.8 + 102224.i −172122. + 55925.8i −499247. + 687155.i −896042. 1.23330e6i 2.50055e6 7.69589e6i 5.42134e6i
2.9 53.1516 + 17.2700i 1186.53 862.066i −10728.1 7794.42i −13864.2 42669.5i 77954.0 25328.8i −759822. + 1.04581e6i −973812. 1.34034e6i −813318. + 2.50313e6i 2.50739e6i
2.10 103.867 + 33.7486i 1680.48 1220.94i −3605.45 2619.51i 2385.75 + 7342.59i 215753. 70102.3i 607900. 836702.i −1.33783e6 1.84137e6i −144697. + 445330.i 843172.i
2.11 178.910 + 58.1314i −2296.87 + 1668.77i 15374.6 + 11170.3i −40945.0 126016.i −507941. + 165040.i −7104.29 + 9778.22i 289708. + 398749.i 1.01278e6 3.11702e6i 2.49256e7i
2.12 186.716 + 60.6678i −624.250 + 453.544i 17927.4 + 13025.0i 24181.1 + 74421.8i −144073. + 46812.2i 68223.2 93901.2i 666478. + 917329.i −1.29403e6 + 3.98262e6i 1.53628e7i
2.13 226.579 + 73.6200i 2991.54 2173.48i 32663.3 + 23731.3i −18469.4 56842.9i 837832. 272228.i −545797. + 751225.i 3.35941e6 + 4.62383e6i 2.74727e6 8.45522e6i 1.42391e7i
6.1 −236.091 + 76.7107i 1404.04 + 1020.09i 36599.6 26591.2i 17129.5 52719.2i −409733. 133130.i 347419. + 478181.i −4.21038e6 + 5.79510e6i −547289. 1.68438e6i 1.37606e7i
6.2 −199.758 + 64.9052i −3456.81 2511.52i 22435.6 16300.4i −9471.22 + 29149.4i 853535. + 277330.i −55107.8 75849.3i −1.40098e6 + 1.92828e6i 4.16378e6 + 1.28148e7i 6.43755e6i
6.3 −157.861 + 51.2920i 79.9689 + 58.1008i 9034.19 6563.72i −14721.0 + 45306.7i −15604.0 5070.06i −565560. 778426.i 509000. 700579.i −1.47500e6 4.53958e6i 7.90722e6i
6.4 −119.417 + 38.8010i 3112.87 + 2261.63i −499.976 + 363.254i −39265.4 + 120847.i −459484. 149295.i 577116. + 794332.i 1.25481e6 1.72710e6i 3.09696e6 + 9.53146e6i 1.59547e7i
6.5 −116.568 + 37.8754i −829.952 602.996i −1101.28 + 800.129i 25059.8 77126.2i 119585. + 38855.5i 411520. + 566408.i 1.27843e6 1.75960e6i −1.15280e6 3.54796e6i 9.93962e6i
6.6 −57.1439 + 18.5672i 2553.58 + 1855.29i −10334.3 + 7508.27i 43338.6 133382.i −180369. 58605.5i −281229. 387078.i 1.02976e6 1.41735e6i 1.60068e6 + 4.92639e6i 8.42667e6i
6.7 −13.9048 + 4.51795i −1467.63 1066.30i −13082.0 + 9504.63i −19976.8 + 61482.1i 25224.6 + 8195.98i 351170. + 483344.i 279760. 385057.i −461067. 1.41902e6i 945153.i
See all 52 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.13
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.d odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 11.15.d.a 52
11.d odd 10 1 inner 11.15.d.a 52
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
11.15.d.a 52 1.a even 1 1 trivial
11.15.d.a 52 11.d odd 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{15}^{\mathrm{new}}(11, [\chi])\).