↑

Properties

Label 532.2.l.b
Level $532$
Weight $2$
Character orbit 532.l
Analytic conductor $4.248$
Analytic rank $0$
Dimension $24$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [532,2,Mod(429,532)] 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("532.429"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(532, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 4])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 532.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.24804138753\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 2 q^{3} - 6 q^{5} - 6 q^{7} + 30 q^{9} + q^{11} - 7 q^{13} - 2 q^{15} - 6 q^{17} + 17 q^{19} - 18 q^{21} - 16 q^{23} - 8 q^{25} + 20 q^{27} - 22 q^{29} - 7 q^{31} + 7 q^{33} - 21 q^{35} + 9 q^{37}+ \cdots - 27 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
429.1 0 −3.17684 0 −1.42518 − 2.46848i 0 1.33785 − 2.28258i 0 7.09231 0
429.2 0 −2.55261 0 −0.292145 − 0.506011i 0 0.854338 + 2.50402i 0 3.51581 0
429.3 0 −2.05389 0 1.16183 + 2.01235i 0 −0.804015 − 2.52063i 0 1.21848 0
429.4 0 −1.21962 0 1.61747 + 2.80155i 0 1.15617 + 2.37976i 0 −1.51253 0
429.5 0 −1.07341 0 −1.76093 − 3.05002i 0 −1.25747 + 2.32783i 0 −1.84780 0
429.6 0 −0.0289013 0 0.260150 + 0.450593i 0 −2.55086 + 0.702209i 0 −2.99916 0
429.7 0 0.197863 0 −1.11568 − 1.93241i 0 −1.27819 − 2.31651i 0 −2.96085 0
429.8 0 1.04126 0 −1.73639 − 3.00752i 0 2.62969 + 0.291052i 0 −1.91577 0
429.9 0 1.54342 0 1.49792 + 2.59447i 0 −2.55868 + 0.673181i 0 −0.617840 0
429.10 0 2.00909 0 0.104422 + 0.180865i 0 0.452777 − 2.60672i 0 1.03645 0
429.11 0 2.98364 0 −0.223039 − 0.386315i 0 1.18643 + 2.36482i 0 5.90209 0
429.12 0 3.32999 0 −1.08843 − 1.88522i 0 −2.16805 − 1.51643i 0 8.08881 0
501.1 0 −3.17684 0 −1.42518 + 2.46848i 0 1.33785 + 2.28258i 0 7.09231 0
501.2 0 −2.55261 0 −0.292145 + 0.506011i 0 0.854338 − 2.50402i 0 3.51581 0
501.3 0 −2.05389 0 1.16183 − 2.01235i 0 −0.804015 + 2.52063i 0 1.21848 0
501.4 0 −1.21962 0 1.61747 − 2.80155i 0 1.15617 − 2.37976i 0 −1.51253 0
501.5 0 −1.07341 0 −1.76093 + 3.05002i 0 −1.25747 − 2.32783i 0 −1.84780 0
501.6 0 −0.0289013 0 0.260150 − 0.450593i 0 −2.55086 − 0.702209i 0 −2.99916 0
501.7 0 0.197863 0 −1.11568 + 1.93241i 0 −1.27819 + 2.31651i 0 −2.96085 0
501.8 0 1.04126 0 −1.73639 + 3.00752i 0 2.62969 − 0.291052i 0 −1.91577 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 429.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
133.g even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 532.2.l.b yes 24
7.c even 3 1 532.2.k.b ✓ 24
19.c even 3 1 532.2.k.b ✓ 24
133.g even 3 1 inner 532.2.l.b yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
532.2.k.b ✓ 24 7.c even 3 1
532.2.k.b ✓ 24 19.c even 3 1
532.2.l.b yes 24 1.a even 1 1 trivial
532.2.l.b yes 24 133.g even 3 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} - T_{3}^{11} - 25 T_{3}^{10} + 20 T_{3}^{9} + 220 T_{3}^{8} - 133 T_{3}^{7} - 825 T_{3}^{6} + \cdots + 4 \) acting on \(S_{2}^{\mathrm{new}}(532, [\chi])\). Copy content Toggle raw display