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Properties

Label 11.11.d.a
Level $11$
Weight $11$
Character orbit 11.d
Analytic conductor $6.989$
Analytic rank $0$
Dimension $36$
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] = [11,11,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, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.2");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 11 \)
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: \(6.98892977941\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 5 q^{2} - 78 q^{3} + 2839 q^{4} + 566 q^{5} - 3525 q^{6} - 9740 q^{7} - 56325 q^{8} + 27883 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 36 q - 5 q^{2} - 78 q^{3} + 2839 q^{4} + 566 q^{5} - 3525 q^{6} - 9740 q^{7} - 56325 q^{8} + 27883 q^{9} - 124277 q^{11} - 690462 q^{12} + 516610 q^{13} - 256990 q^{14} + 965070 q^{15} + 1558071 q^{16} - 1563930 q^{17} - 3716190 q^{18} + 6441265 q^{19} + 11846024 q^{20} - 38364515 q^{22} + 2991652 q^{23} - 6935455 q^{24} + 53140199 q^{25} + 53101970 q^{26} - 8464269 q^{27} - 158441860 q^{28} - 30773770 q^{29} + 164452420 q^{30} + 63499996 q^{31} - 337126483 q^{33} + 8404770 q^{34} + 93755030 q^{35} + 17054342 q^{36} - 20015352 q^{37} + 222215700 q^{38} + 13696700 q^{39} + 66388740 q^{40} + 168755230 q^{41} - 14778490 q^{42} + 1092554652 q^{44} - 1073801424 q^{45} - 843022850 q^{46} - 1466232 q^{47} - 1407287968 q^{48} - 247720591 q^{49} + 1888812255 q^{50} + 2730932925 q^{51} - 1016067090 q^{52} - 1574434638 q^{53} + 1667070934 q^{55} + 464386660 q^{56} - 1846600035 q^{57} - 5738108180 q^{58} - 3108186601 q^{59} + 1748753840 q^{60} + 4185015940 q^{61} + 8028589520 q^{62} + 5208740790 q^{63} - 568398521 q^{64} - 2767952130 q^{66} - 6673767122 q^{67} - 12578329400 q^{68} + 1374718982 q^{69} - 10858899380 q^{70} + 5532218182 q^{71} + 14192383525 q^{72} + 6815310530 q^{73} + 27099775830 q^{74} + 5359754505 q^{75} - 17322154610 q^{77} - 35448700760 q^{78} - 28511789960 q^{79} + 9512354316 q^{80} - 16645589156 q^{81} + 4251999505 q^{82} + 6078874665 q^{83} + 75048937530 q^{84} + 52883120010 q^{85} - 11116561805 q^{86} - 35103955205 q^{88} - 19181286322 q^{89} - 98405028320 q^{90} - 22561214930 q^{91} - 78730839752 q^{92} + 17679006934 q^{93} + 94886813720 q^{94} + 79444332050 q^{95} + 162737230420 q^{96} - 7866178077 q^{97} - 15303258335 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −59.0856 − 19.1981i −169.636 + 123.248i 2294.11 + 1666.77i 231.636 + 712.903i 12389.1 − 4025.48i −12948.0 + 17821.4i −66156.6 − 91056.8i −4660.83 + 14344.5i − 46569.2i
2.2 −41.5867 − 13.5123i 264.923 − 192.478i 718.438 + 521.976i 1375.98 + 4234.82i −13618.1 + 4424.78i 16723.5 − 23017.9i 3494.49 + 4809.75i 14889.2 − 45824.3i − 194705.i
2.3 −30.7987 − 10.0071i 42.4807 − 30.8641i 19.9828 + 14.5184i −910.975 − 2803.69i −1617.21 + 525.463i −2349.92 + 3234.39i 19021.3 + 26180.6i −17395.1 + 53536.7i 95466.2i
2.4 −17.2362 − 5.60038i −324.230 + 235.567i −562.712 − 408.834i 388.585 + 1195.94i 6907.76 − 2244.47i 4143.10 − 5702.49i 18317.6 + 25212.0i 31386.3 − 96597.2i − 22789.7i
2.5 7.33771 + 2.38417i 359.258 − 261.016i −780.276 − 566.903i −643.352 − 1980.03i 3258.43 − 1058.73i −13144.2 + 18091.5i −9017.63 − 12411.7i 42689.6 − 131385.i − 16062.8i
2.6 10.1053 + 3.28341i 3.00272 − 2.18160i −737.097 − 535.532i 1584.60 + 4876.89i 37.5064 − 12.1866i −6065.96 + 8349.08i −12085.5 − 16634.3i −18242.9 + 56145.8i 54485.2i
2.7 20.9759 + 6.81550i −72.2310 + 52.4789i −434.894 − 315.969i −1002.36 − 3084.94i −1872.78 + 608.504i 10404.0 − 14319.9i −20243.8 − 27863.2i −15783.9 + 48577.7i − 71541.1i
2.8 47.2775 + 15.3614i −306.236 + 222.494i 1170.75 + 850.603i −217.651 − 669.862i −17895.9 + 5814.73i −14863.0 + 20457.1i 12363.5 + 17017.0i 26030.1 − 80112.4i − 35012.8i
2.9 48.9033 + 15.8897i 165.281 − 120.084i 1310.62 + 952.222i 259.656 + 799.138i 9990.90 − 3246.24i 6472.97 − 8909.28i 18014.0 + 24794.1i −5349.36 + 16463.6i 43206.3i
6.1 −59.0856 + 19.1981i −169.636 − 123.248i 2294.11 − 1666.77i 231.636 − 712.903i 12389.1 + 4025.48i −12948.0 − 17821.4i −66156.6 + 91056.8i −4660.83 − 14344.5i 46569.2i
6.2 −41.5867 + 13.5123i 264.923 + 192.478i 718.438 − 521.976i 1375.98 − 4234.82i −13618.1 − 4424.78i 16723.5 + 23017.9i 3494.49 − 4809.75i 14889.2 + 45824.3i 194705.i
6.3 −30.7987 + 10.0071i 42.4807 + 30.8641i 19.9828 − 14.5184i −910.975 + 2803.69i −1617.21 − 525.463i −2349.92 − 3234.39i 19021.3 − 26180.6i −17395.1 − 53536.7i − 95466.2i
6.4 −17.2362 + 5.60038i −324.230 − 235.567i −562.712 + 408.834i 388.585 − 1195.94i 6907.76 + 2244.47i 4143.10 + 5702.49i 18317.6 − 25212.0i 31386.3 + 96597.2i 22789.7i
6.5 7.33771 − 2.38417i 359.258 + 261.016i −780.276 + 566.903i −643.352 + 1980.03i 3258.43 + 1058.73i −13144.2 − 18091.5i −9017.63 + 12411.7i 42689.6 + 131385.i 16062.8i
6.6 10.1053 − 3.28341i 3.00272 + 2.18160i −737.097 + 535.532i 1584.60 − 4876.89i 37.5064 + 12.1866i −6065.96 − 8349.08i −12085.5 + 16634.3i −18242.9 − 56145.8i − 54485.2i
6.7 20.9759 − 6.81550i −72.2310 − 52.4789i −434.894 + 315.969i −1002.36 + 3084.94i −1872.78 − 608.504i 10404.0 + 14319.9i −20243.8 + 27863.2i −15783.9 − 48577.7i 71541.1i
6.8 47.2775 − 15.3614i −306.236 − 222.494i 1170.75 − 850.603i −217.651 + 669.862i −17895.9 − 5814.73i −14863.0 − 20457.1i 12363.5 − 17017.0i 26030.1 + 80112.4i 35012.8i
6.9 48.9033 − 15.8897i 165.281 + 120.084i 1310.62 − 952.222i 259.656 − 799.138i 9990.90 + 3246.24i 6472.97 + 8909.28i 18014.0 − 24794.1i −5349.36 − 16463.6i − 43206.3i
7.1 −33.5930 + 46.2368i −56.5936 + 174.177i −692.917 − 2132.58i −4779.99 + 3472.86i −6152.24 − 8467.83i 9381.68 − 3048.29i 66221.7 + 21516.7i 20636.8 + 14993.5i − 337675.i
7.2 −27.8622 + 38.3491i 18.5771 − 57.1744i −377.914 − 1163.10i 4143.06 − 3010.11i 1674.98 + 2305.42i −6688.23 + 2173.14i 8969.30 + 2914.30i 44847.8 + 32583.9i 242751.i
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.9
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 11.11.d.a ✓ 36
3.b odd 2 1 99.11.k.a 36
11.c even 5 1 121.11.b.c 36
11.d odd 10 1 inner 11.11.d.a ✓ 36
11.d odd 10 1 121.11.b.c 36
33.f even 10 1 99.11.k.a 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
11.11.d.a ✓ 36 1.a even 1 1 trivial
11.11.d.a ✓ 36 11.d odd 10 1 inner
99.11.k.a 36 3.b odd 2 1
99.11.k.a 36 33.f even 10 1
121.11.b.c 36 11.c even 5 1
121.11.b.c 36 11.d odd 10 1

Hecke kernels

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