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Properties

Label 105.5.e.a
Level $105$
Weight $5$
Character orbit 105.e
Analytic conductor $10.854$
Analytic rank $0$
Dimension $32$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [105,5,Mod(34,105)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("105.34"); S:= CuspForms(chi, 5); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 5, names="a")
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 105.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.8538461238\)
Analytic rank: \(0\)
Dimension: \(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 256 q^{4} + 864 q^{9} + 168 q^{11} + 588 q^{14} + 144 q^{15} + 944 q^{16} + 396 q^{21} - 3256 q^{25} + 864 q^{29} + 3024 q^{30} - 444 q^{35} - 6912 q^{36} + 216 q^{39} + 4824 q^{44} + 25008 q^{46}+ \cdots + 4536 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
34.1 − 7.63204i −5.19615 −42.2480 −0.322863 − 24.9979i 39.6572i 5.28112 + 48.7146i 200.326i 27.0000 −190.785 + 2.46410i
34.2 − 7.63204i 5.19615 −42.2480 0.322863 + 24.9979i − 39.6572i −5.28112 + 48.7146i 200.326i 27.0000 190.785 − 2.46410i
34.3 − 6.29647i −5.19615 −23.6455 −23.5093 + 8.50375i 32.7174i −46.8756 − 14.2714i 48.1400i 27.0000 53.5436 + 148.026i
34.4 − 6.29647i 5.19615 −23.6455 23.5093 − 8.50375i − 32.7174i 46.8756 − 14.2714i 48.1400i 27.0000 −53.5436 − 148.026i
34.5 − 5.89598i −5.19615 −18.7625 9.19226 + 23.2487i 30.6364i 47.1764 + 13.2433i 16.2879i 27.0000 137.074 − 54.1974i
34.6 − 5.89598i 5.19615 −18.7625 −9.19226 − 23.2487i − 30.6364i −47.1764 + 13.2433i 16.2879i 27.0000 −137.074 + 54.1974i
34.7 − 5.52056i −5.19615 −14.4765 16.5868 − 18.7050i 28.6857i 0.191033 − 48.9996i − 8.41031i 27.0000 −103.262 − 91.5682i
34.8 − 5.52056i 5.19615 −14.4765 −16.5868 + 18.7050i − 28.6857i −0.191033 − 48.9996i − 8.41031i 27.0000 103.262 + 91.5682i
34.9 − 3.68935i −5.19615 2.38872 −17.0477 − 18.2859i 19.1704i 44.0892 − 21.3809i − 67.8424i 27.0000 −67.4631 + 62.8950i
34.10 − 3.68935i 5.19615 2.38872 17.0477 + 18.2859i − 19.1704i −44.0892 − 21.3809i − 67.8424i 27.0000 67.4631 − 62.8950i
34.11 − 3.00009i −5.19615 6.99947 20.9370 − 13.6617i 15.5889i −24.3551 + 42.5186i − 69.0004i 27.0000 −40.9862 − 62.8129i
34.12 − 3.00009i 5.19615 6.99947 −20.9370 + 13.6617i − 15.5889i 24.3551 + 42.5186i − 69.0004i 27.0000 40.9862 + 62.8129i
34.13 − 2.44594i −5.19615 10.0174 7.22188 + 23.9342i 12.7095i −46.9408 + 14.0558i − 63.6369i 27.0000 58.5415 − 17.6643i
34.14 − 2.44594i 5.19615 10.0174 −7.22188 − 23.9342i − 12.7095i 46.9408 + 14.0558i − 63.6369i 27.0000 −58.5415 + 17.6643i
34.15 − 0.522389i −5.19615 15.7271 −19.9863 + 15.0183i 2.71441i 2.38113 − 48.9421i − 16.5739i 27.0000 7.84539 + 10.4406i
34.16 − 0.522389i 5.19615 15.7271 19.9863 − 15.0183i − 2.71441i −2.38113 − 48.9421i − 16.5739i 27.0000 −7.84539 − 10.4406i
34.17 0.522389i −5.19615 15.7271 −19.9863 − 15.0183i − 2.71441i 2.38113 + 48.9421i 16.5739i 27.0000 7.84539 − 10.4406i
34.18 0.522389i 5.19615 15.7271 19.9863 + 15.0183i 2.71441i −2.38113 + 48.9421i 16.5739i 27.0000 −7.84539 + 10.4406i
34.19 2.44594i −5.19615 10.0174 7.22188 − 23.9342i − 12.7095i −46.9408 − 14.0558i 63.6369i 27.0000 58.5415 + 17.6643i
34.20 2.44594i 5.19615 10.0174 −7.22188 + 23.9342i 12.7095i 46.9408 − 14.0558i 63.6369i 27.0000 −58.5415 − 17.6643i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 34.32
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
7.b odd 2 1 inner
35.c odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.5.e.a ✓ 32
3.b odd 2 1 315.5.e.f 32
5.b even 2 1 inner 105.5.e.a ✓ 32
5.c odd 4 2 525.5.h.e 32
7.b odd 2 1 inner 105.5.e.a ✓ 32
15.d odd 2 1 315.5.e.f 32
21.c even 2 1 315.5.e.f 32
35.c odd 2 1 inner 105.5.e.a ✓ 32
35.f even 4 2 525.5.h.e 32
105.g even 2 1 315.5.e.f 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.5.e.a ✓ 32 1.a even 1 1 trivial
105.5.e.a ✓ 32 5.b even 2 1 inner
105.5.e.a ✓ 32 7.b odd 2 1 inner
105.5.e.a ✓ 32 35.c odd 2 1 inner
315.5.e.f 32 3.b odd 2 1
315.5.e.f 32 15.d odd 2 1
315.5.e.f 32 21.c even 2 1
315.5.e.f 32 105.g even 2 1
525.5.h.e 32 5.c odd 4 2
525.5.h.e 32 35.f even 4 2

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(105, [\chi])\).