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Properties

Label 460.4.c.a
Level $460$
Weight $4$
Character orbit 460.c
Analytic conductor $27.141$
Analytic rank $0$
Dimension $32$
Inner twists $2$

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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] = [460,4,Mod(369,460)] 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("460.369"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(460, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 460.c (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: \(27.1408786026\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 12 q^{5} - 220 q^{9} - 8 q^{11} - 168 q^{15} + 144 q^{19} - 32 q^{21} + 100 q^{25} - 76 q^{29} + 652 q^{31} + 320 q^{35} - 1128 q^{39} - 560 q^{41} + 1208 q^{45} - 2224 q^{49} + 3192 q^{51} - 1304 q^{55}+ \cdots + 1952 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
369.1 0 − 9.99558i 0 −4.59737 − 10.1914i 0 22.9508i 0 −72.9116 0
369.2 0 − 9.40839i 0 −11.1755 + 0.327370i 0 − 22.7593i 0 −61.5178 0
369.3 0 − 8.27761i 0 8.53082 − 7.22669i 0 − 19.6800i 0 −41.5188 0
369.4 0 − 7.81841i 0 −4.79378 + 10.1005i 0 6.53013i 0 −34.1276 0
369.5 0 − 6.52653i 0 11.0335 − 1.80587i 0 34.5907i 0 −15.5956 0
369.6 0 − 6.51398i 0 2.07704 − 10.9857i 0 − 2.24515i 0 −15.4319 0
369.7 0 − 6.05177i 0 11.1311 + 1.04775i 0 − 20.6013i 0 −9.62397 0
369.8 0 − 5.50846i 0 −4.90177 + 10.0485i 0 16.7469i 0 −3.34309 0
369.9 0 − 4.94851i 0 −10.0491 + 4.90060i 0 − 15.6910i 0 2.51221 0
369.10 0 − 3.93269i 0 2.34865 + 10.9309i 0 − 29.6587i 0 11.5340 0
369.11 0 − 3.67762i 0 −10.4963 − 3.85079i 0 21.0303i 0 13.4751 0
369.12 0 − 3.51185i 0 −9.49311 − 5.90600i 0 − 1.79731i 0 14.6669 0
369.13 0 − 1.97415i 0 11.0164 + 1.90734i 0 13.0256i 0 23.1027 0
369.14 0 − 1.27714i 0 1.12516 − 11.1236i 0 16.7357i 0 25.3689 0
369.15 0 − 0.709976i 0 −5.09471 − 9.95208i 0 − 33.8714i 0 26.4959 0
369.16 0 − 0.292148i 0 7.33884 + 8.43454i 0 7.10909i 0 26.9146 0
369.17 0 0.292148i 0 7.33884 − 8.43454i 0 − 7.10909i 0 26.9146 0
369.18 0 0.709976i 0 −5.09471 + 9.95208i 0 33.8714i 0 26.4959 0
369.19 0 1.27714i 0 1.12516 + 11.1236i 0 − 16.7357i 0 25.3689 0
369.20 0 1.97415i 0 11.0164 − 1.90734i 0 − 13.0256i 0 23.1027 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 369.32
Significant digits:
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Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 460.4.c.a ✓ 32
5.b even 2 1 inner 460.4.c.a ✓ 32
5.c odd 4 1 2300.4.a.k 16
5.c odd 4 1 2300.4.a.l 16
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
460.4.c.a ✓ 32 1.a even 1 1 trivial
460.4.c.a ✓ 32 5.b even 2 1 inner
2300.4.a.k 16 5.c odd 4 1
2300.4.a.l 16 5.c odd 4 1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(460, [\chi])\).