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Properties

Label 95.7.d.d
Level $95$
Weight $7$
Character orbit 95.d
Analytic conductor $21.855$
Analytic rank $0$
Dimension $48$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,7,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, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.94");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
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: \(21.8551379439\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 1536 q^{4} + 108 q^{5} - 584 q^{6} + 8744 q^{9} - 2632 q^{11} + 21400 q^{16} + 19272 q^{19} + 16764 q^{20} + 115608 q^{24} - 106796 q^{25} - 78264 q^{26} - 243704 q^{30} + 197584 q^{35} - 645576 q^{36}+ \cdots + 3267896 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
94.1 −15.6013 −14.3779 179.401 52.9095 − 113.250i 224.314 619.509i −1800.41 −522.275 −825.458 + 1766.85i
94.2 −15.6013 −14.3779 179.401 52.9095 + 113.250i 224.314 − 619.509i −1800.41 −522.275 −825.458 − 1766.85i
94.3 −13.6197 22.4793 121.496 94.0230 − 82.3692i −306.161 − 388.532i −783.074 −223.681 −1280.56 + 1121.84i
94.4 −13.6197 22.4793 121.496 94.0230 + 82.3692i −306.161 388.532i −783.074 −223.681 −1280.56 − 1121.84i
94.5 −13.1881 −37.6588 109.927 −67.2707 − 105.355i 496.649 − 324.825i −605.685 689.186 887.174 + 1389.43i
94.6 −13.1881 −37.6588 109.927 −67.2707 + 105.355i 496.649 324.825i −605.685 689.186 887.174 − 1389.43i
94.7 −12.5212 7.08147 92.7798 −100.653 − 74.1219i −88.6683 − 86.3202i −360.356 −678.853 1260.29 + 928.093i
94.8 −12.5212 7.08147 92.7798 −100.653 + 74.1219i −88.6683 86.3202i −360.356 −678.853 1260.29 − 928.093i
94.9 −11.2109 40.4769 61.6844 68.6103 − 104.487i −453.783 223.504i 25.9597 909.379 −769.184 + 1171.40i
94.10 −11.2109 40.4769 61.6844 68.6103 + 104.487i −453.783 − 223.504i 25.9597 909.379 −769.184 − 1171.40i
94.11 −7.97374 −10.4283 −0.419420 81.2537 − 94.9886i 83.1524 − 400.633i 513.664 −620.251 −647.896 + 757.415i
94.12 −7.97374 −10.4283 −0.419420 81.2537 + 94.9886i 83.1524 400.633i 513.664 −620.251 −647.896 − 757.415i
94.13 −7.28171 23.1081 −10.9768 −80.3125 − 95.7857i −168.266 430.723i 545.959 −195.016 584.812 + 697.483i
94.14 −7.28171 23.1081 −10.9768 −80.3125 + 95.7857i −168.266 − 430.723i 545.959 −195.016 584.812 − 697.483i
94.15 −6.98433 −15.2192 −15.2191 11.0350 − 124.512i 106.296 344.183i 553.292 −497.377 −77.0722 + 869.633i
94.16 −6.98433 −15.2192 −15.2191 11.0350 + 124.512i 106.296 − 344.183i 553.292 −497.377 −77.0722 − 869.633i
94.17 −6.74131 45.9005 −18.5547 −72.3540 − 101.931i −309.430 − 495.038i 556.527 1377.86 487.761 + 687.147i
94.18 −6.74131 45.9005 −18.5547 −72.3540 + 101.931i −309.430 495.038i 556.527 1377.86 487.761 − 687.147i
94.19 −6.41263 −35.7503 −22.8782 −121.536 − 29.2230i 229.254 513.890i 557.118 549.086 779.366 + 187.396i
94.20 −6.41263 −35.7503 −22.8782 −121.536 + 29.2230i 229.254 − 513.890i 557.118 549.086 779.366 − 187.396i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 94.48
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 95.7.d.d ✓ 48
5.b even 2 1 inner 95.7.d.d ✓ 48
19.b odd 2 1 inner 95.7.d.d ✓ 48
95.d odd 2 1 inner 95.7.d.d ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.7.d.d ✓ 48 1.a even 1 1 trivial
95.7.d.d ✓ 48 5.b even 2 1 inner
95.7.d.d ✓ 48 19.b odd 2 1 inner
95.7.d.d ✓ 48 95.d odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} - 1152 T_{2}^{22} + 574861 T_{2}^{20} - 163495126 T_{2}^{18} + 29354980192 T_{2}^{16} + \cdots + 25\!\cdots\!00 \) acting on \(S_{7}^{\mathrm{new}}(95, [\chi])\). Copy content Toggle raw display