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Properties

Label 95.11.d.d
Level $95$
Weight $11$
Character orbit 95.d
Analytic conductor $60.359$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,11,Mod(94,95)]
 
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([1, 1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.94");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 95.d (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: \(88\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 88 q + 44224 q^{4} - 2842 q^{5} + 760 q^{6} + 1495904 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 88 q + 44224 q^{4} - 2842 q^{5} + 760 q^{6} + 1495904 q^{9} + 276452 q^{11} + 12835608 q^{16} + 6481056 q^{19} + 10691004 q^{20} + 111261336 q^{24} - 82580066 q^{25} - 147773496 q^{26} - 34766744 q^{30} - 75337666 q^{35} + 1334345592 q^{36} + 134353720 q^{39} - 403880392 q^{44} + 72819522 q^{45} - 6680182804 q^{49} - 3326634584 q^{54} - 364133590 q^{55} - 4243415388 q^{61} + 954601224 q^{64} - 23355039776 q^{66} - 14144890080 q^{74} + 13010503336 q^{76} - 38804958720 q^{80} + 3737726568 q^{81} - 20627379542 q^{85} + 69719838022 q^{95} + 19008194008 q^{96} - 174222077812 q^{99}+O(q^{100}) \) 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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
94.1 −61.7115 −173.365 2784.31 −2056.39 − 2353.05i 10698.6 − 21560.7i −108631. −28993.5 126903. + 145211.i
94.2 −61.7115 −173.365 2784.31 −2056.39 + 2353.05i 10698.6 21560.7i −108631. −28993.5 126903. − 145211.i
94.3 −57.7069 289.850 2306.09 −1944.80 − 2446.10i −16726.4 11532.1i −73985.6 24964.1 112228. + 141157.i
94.4 −57.7069 289.850 2306.09 −1944.80 + 2446.10i −16726.4 − 11532.1i −73985.6 24964.1 112228. − 141157.i
94.5 −56.0719 −445.973 2120.05 −62.3147 − 3124.38i 25006.5 25024.8i −61457.8 139843. 3494.10 + 175190.i
94.6 −56.0719 −445.973 2120.05 −62.3147 + 3124.38i 25006.5 − 25024.8i −61457.8 139843. 3494.10 − 175190.i
94.7 −55.8101 433.253 2090.76 1961.95 − 2432.36i −24179.9 − 30878.8i −59536.0 128660. −109496. + 135750.i
94.8 −55.8101 433.253 2090.76 1961.95 + 2432.36i −24179.9 30878.8i −59536.0 128660. −109496. − 135750.i
94.9 −53.9549 −315.189 1887.14 2668.83 − 1625.72i 17006.0 − 17879.0i −46570.4 40295.1 −143997. + 87715.5i
94.10 −53.9549 −315.189 1887.14 2668.83 + 1625.72i 17006.0 17879.0i −46570.4 40295.1 −143997. − 87715.5i
94.11 −52.2594 37.2886 1707.05 2000.35 − 2400.88i −1948.68 18651.6i −35695.7 −57658.6 −104537. + 125469.i
94.12 −52.2594 37.2886 1707.05 2000.35 + 2400.88i −1948.68 − 18651.6i −35695.7 −57658.6 −104537. − 125469.i
94.13 −49.2250 44.2796 1399.10 616.697 − 3063.55i −2179.66 8879.95i −18464.4 −57088.3 −30356.9 + 150803.i
94.14 −49.2250 44.2796 1399.10 616.697 + 3063.55i −2179.66 − 8879.95i −18464.4 −57088.3 −30356.9 − 150803.i
94.15 −48.2121 −193.876 1300.41 −2707.21 − 1560.98i 9347.15 7555.06i −13326.1 −21461.2 130520. + 75258.1i
94.16 −48.2121 −193.876 1300.41 −2707.21 + 1560.98i 9347.15 − 7555.06i −13326.1 −21461.2 130520. − 75258.1i
94.17 −39.9079 24.7349 568.644 −348.110 − 3105.55i −987.121 − 29317.3i 18172.3 −58437.2 13892.3 + 123936.i
94.18 −39.9079 24.7349 568.644 −348.110 + 3105.55i −987.121 29317.3i 18172.3 −58437.2 13892.3 − 123936.i
94.19 −39.2205 299.547 514.248 2852.87 − 1275.44i −11748.4 6661.49i 19992.7 30679.7 −111891. + 50023.2i
94.20 −39.2205 299.547 514.248 2852.87 + 1275.44i −11748.4 − 6661.49i 19992.7 30679.7 −111891. − 50023.2i
See all 88 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 94.88
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
19.b odd 2 1 inner
95.d 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.d.d ✓ 88
5.b even 2 1 inner 95.11.d.d ✓ 88
19.b odd 2 1 inner 95.11.d.d ✓ 88
95.d odd 2 1 inner 95.11.d.d ✓ 88
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.11.d.d ✓ 88 1.a even 1 1 trivial
95.11.d.d ✓ 88 5.b even 2 1 inner
95.11.d.d ✓ 88 19.b odd 2 1 inner
95.11.d.d ✓ 88 95.d odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{44} - 33584 T_{2}^{42} + 522287389 T_{2}^{40} - 4993908210438 T_{2}^{38} + \cdots + 21\!\cdots\!00 \) acting on \(S_{11}^{\mathrm{new}}(95, [\chi])\). Copy content Toggle raw display