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Properties

Label 936.2.m.i
Level $936$
Weight $2$
Character orbit 936.m
Analytic conductor $7.474$
Analytic rank $0$
Dimension $24$
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] = [936,2,Mod(181,936)] 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("936.181"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 936.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.47399762919\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 312)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{10} - 16 q^{14} + 28 q^{16} - 32 q^{17} - 44 q^{22} + 40 q^{25} - 16 q^{38} + 12 q^{40} - 72 q^{49} - 12 q^{52} + 16 q^{55} + 32 q^{56} + 88 q^{62} + 24 q^{64} + 8 q^{68} + 24 q^{74} - 64 q^{79}+ \cdots + 128 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
181.1 −1.41087 − 0.0972570i 0 1.98108 + 0.274433i −0.859867 0 − 2.42446i −2.76835 − 0.579863i 0 1.21316 + 0.0836282i
181.2 −1.41087 + 0.0972570i 0 1.98108 − 0.274433i −0.859867 0 2.42446i −2.76835 + 0.579863i 0 1.21316 − 0.0836282i
181.3 −1.35838 − 0.393457i 0 1.69038 + 1.06893i 3.70799 0 4.20506i −1.87560 − 2.11710i 0 −5.03685 − 1.45893i
181.4 −1.35838 + 0.393457i 0 1.69038 − 1.06893i 3.70799 0 − 4.20506i −1.87560 + 2.11710i 0 −5.03685 + 1.45893i
181.5 −1.23796 − 0.683714i 0 1.06507 + 1.69282i −3.44141 0 − 2.84073i −0.161106 − 2.82384i 0 4.26031 + 2.35294i
181.6 −1.23796 + 0.683714i 0 1.06507 − 1.69282i −3.44141 0 2.84073i −0.161106 + 2.82384i 0 4.26031 − 2.35294i
181.7 −0.557063 − 1.29988i 0 −1.37936 + 1.44823i 0.172184 0 1.91402i 2.65091 + 0.986248i 0 −0.0959176 − 0.223819i
181.8 −0.557063 + 1.29988i 0 −1.37936 − 1.44823i 0.172184 0 − 1.91402i 2.65091 − 0.986248i 0 −0.0959176 + 0.223819i
181.9 −0.486010 − 1.32808i 0 −1.52759 + 1.29092i 3.48777 0 0.644203i 2.45687 + 1.40136i 0 −1.69509 − 4.63204i
181.10 −0.486010 + 1.32808i 0 −1.52759 − 1.29092i 3.48777 0 − 0.644203i 2.45687 − 1.40136i 0 −1.69509 + 4.63204i
181.11 −0.291905 − 1.38376i 0 −1.82958 + 0.807852i −1.21406 0 − 4.92861i 1.65194 + 2.29589i 0 0.354391 + 1.67997i
181.12 −0.291905 + 1.38376i 0 −1.82958 − 0.807852i −1.21406 0 4.92861i 1.65194 − 2.29589i 0 0.354391 − 1.67997i
181.13 0.291905 − 1.38376i 0 −1.82958 − 0.807852i 1.21406 0 − 4.92861i −1.65194 + 2.29589i 0 0.354391 − 1.67997i
181.14 0.291905 + 1.38376i 0 −1.82958 + 0.807852i 1.21406 0 4.92861i −1.65194 − 2.29589i 0 0.354391 + 1.67997i
181.15 0.486010 − 1.32808i 0 −1.52759 − 1.29092i −3.48777 0 0.644203i −2.45687 + 1.40136i 0 −1.69509 + 4.63204i
181.16 0.486010 + 1.32808i 0 −1.52759 + 1.29092i −3.48777 0 − 0.644203i −2.45687 − 1.40136i 0 −1.69509 − 4.63204i
181.17 0.557063 − 1.29988i 0 −1.37936 − 1.44823i −0.172184 0 1.91402i −2.65091 + 0.986248i 0 −0.0959176 + 0.223819i
181.18 0.557063 + 1.29988i 0 −1.37936 + 1.44823i −0.172184 0 − 1.91402i −2.65091 − 0.986248i 0 −0.0959176 − 0.223819i
181.19 1.23796 − 0.683714i 0 1.06507 − 1.69282i 3.44141 0 − 2.84073i 0.161106 − 2.82384i 0 4.26031 − 2.35294i
181.20 1.23796 + 0.683714i 0 1.06507 + 1.69282i 3.44141 0 2.84073i 0.161106 + 2.82384i 0 4.26031 + 2.35294i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 181.24
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.b even 2 1 inner
13.b even 2 1 inner
104.e even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 936.2.m.i 24
3.b odd 2 1 312.2.m.c ✓ 24
4.b odd 2 1 3744.2.m.i 24
8.b even 2 1 inner 936.2.m.i 24
8.d odd 2 1 3744.2.m.i 24
12.b even 2 1 1248.2.m.c 24
13.b even 2 1 inner 936.2.m.i 24
24.f even 2 1 1248.2.m.c 24
24.h odd 2 1 312.2.m.c ✓ 24
39.d odd 2 1 312.2.m.c ✓ 24
52.b odd 2 1 3744.2.m.i 24
104.e even 2 1 inner 936.2.m.i 24
104.h odd 2 1 3744.2.m.i 24
156.h even 2 1 1248.2.m.c 24
312.b odd 2 1 312.2.m.c ✓ 24
312.h even 2 1 1248.2.m.c 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
312.2.m.c ✓ 24 3.b odd 2 1
312.2.m.c ✓ 24 24.h odd 2 1
312.2.m.c ✓ 24 39.d odd 2 1
312.2.m.c ✓ 24 312.b odd 2 1
936.2.m.i 24 1.a even 1 1 trivial
936.2.m.i 24 8.b even 2 1 inner
936.2.m.i 24 13.b even 2 1 inner
936.2.m.i 24 104.e even 2 1 inner
1248.2.m.c 24 12.b even 2 1
1248.2.m.c 24 24.f even 2 1
1248.2.m.c 24 156.h even 2 1
1248.2.m.c 24 312.h even 2 1
3744.2.m.i 24 4.b odd 2 1
3744.2.m.i 24 8.d odd 2 1
3744.2.m.i 24 52.b odd 2 1
3744.2.m.i 24 104.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} - 40T_{5}^{10} + 560T_{5}^{8} - 3088T_{5}^{6} + 4992T_{5}^{4} - 2304T_{5}^{2} + 64 \) acting on \(S_{2}^{\mathrm{new}}(936, [\chi])\). Copy content Toggle raw display