Properties

Label 95.11.c.a
Level $95$
Weight $11$
Character orbit 95.c
Analytic conductor $60.359$
Analytic rank $0$
Dimension $68$
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(56,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(2))
 
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("95.56");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 95.c (of order \(2\), degree \(1\), 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: \(68\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 68 q - 35644 q^{4} - 2044 q^{6} + 76620 q^{7} - 1353552 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 68 q - 35644 q^{4} - 2044 q^{6} + 76620 q^{7} - 1353552 q^{9} - 418144 q^{11} + 21763300 q^{16} - 10023236 q^{17} + 518264 q^{19} + 4962204 q^{23} + 2604244 q^{24} + 132812500 q^{25} + 32178588 q^{26} - 109025284 q^{28} + 39875000 q^{30} + 39875000 q^{35} + 420547696 q^{36} - 504912596 q^{38} + 51693988 q^{39} + 343589380 q^{42} + 72617360 q^{43} - 846875584 q^{44} + 148625000 q^{45} + 426767656 q^{47} + 3802641528 q^{49} + 594603476 q^{54} - 361360620 q^{57} - 1963881788 q^{58} + 7470512872 q^{61} - 2514646024 q^{62} - 6611740944 q^{63} - 13094608884 q^{64} + 9558616040 q^{66} + 17177918780 q^{68} - 2447766556 q^{73} - 1842337832 q^{74} - 5604056776 q^{76} - 320485400 q^{77} - 821875000 q^{80} + 5162401956 q^{81} - 17137563304 q^{82} - 14922506320 q^{83} - 4799500000 q^{85} + 5085654996 q^{87} - 27413957236 q^{92} - 11067885256 q^{93} + 1613500000 q^{95} - 67563054044 q^{96} + 76070139768 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
56.1 62.1919i 381.522i −2843.84 −1397.54 −23727.6 −5606.85 113179.i −86509.7 86915.9i
56.2 61.7537i 249.725i −2789.52 1397.54 −15421.4 30173.4 109028.i −3313.41 86303.5i
56.3 59.8034i 69.3732i −2552.45 −1397.54 4148.75 −21925.2 91406.6i 54236.4 83577.8i
56.4 59.4439i 262.238i −2509.58 1397.54 15588.5 13097.9 88308.7i −9719.86 83075.4i
56.5 58.8412i 322.019i −2438.29 1397.54 18948.0 −14394.2 83218.3i −44647.2 82233.1i
56.6 56.3762i 430.055i −2154.27 −1397.54 24244.8 15010.3 63720.6i −125898. 78788.1i
56.7 55.5930i 228.918i −2066.58 1397.54 −12726.3 −20724.8 57960.4i 6645.37 77693.6i
56.8 52.8152i 180.092i −1765.45 −1397.54 −9511.57 22409.1 39159.6i 26616.0 73811.5i
56.9 49.9636i 275.923i −1472.36 −1397.54 13786.1 451.343 22401.8i −17084.7 69826.3i
56.10 49.5166i 99.2692i −1427.90 1397.54 −4915.48 −5912.68 19999.7i 49194.6 69201.6i
56.11 49.4757i 10.8416i −1423.84 −1397.54 536.394 13282.9 19782.5i 58931.5 69144.4i
56.12 45.0974i 233.570i −1009.78 1397.54 10533.4 29576.4 641.391i 4493.86 63025.6i
56.13 44.6372i 337.722i −968.483 −1397.54 −15075.0 −20874.9 2478.12i −55007.3 62382.4i
56.14 42.8761i 436.600i −814.356 1397.54 −18719.7 16685.1 8988.69i −131571. 59921.1i
56.15 42.0113i 256.740i −740.946 1397.54 10786.0 −9164.39 11891.4i −6866.66 58712.5i
56.16 40.7068i 92.7742i −633.046 −1397.54 3776.54 −29798.5 15914.5i 50441.9 56889.5i
56.17 39.1187i 305.024i −506.271 −1397.54 −11932.1 11384.7 20252.9i −33990.7 54670.0i
56.18 32.6481i 41.6316i −41.8959 1397.54 1359.19 −15608.7 32063.8i 57315.8 45627.1i
56.19 30.4924i 355.876i 94.2110 −1397.54 10851.5 −1797.03 34097.0i −67598.8 42614.5i
56.20 29.0491i 463.924i 180.148 1397.54 13476.6 20091.2 34979.5i −156176. 40597.4i
See all 68 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 56.68
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.11.c.a 68
19.b odd 2 1 inner 95.11.c.a 68
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.11.c.a 68 1.a even 1 1 trivial
95.11.c.a 68 19.b odd 2 1 inner

Hecke kernels

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