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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [7935,2,Mod(1,7935)] 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("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7935.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [25,11,25,31,25,11,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(63.3612940039\)
Analytic rank: \(0\)
Dimension: \(25\)
Twist minimal: no (minimal twist has level 345)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} + 25 q^{5} + 11 q^{6} + 7 q^{7} + 33 q^{8} + 25 q^{9} + 11 q^{10} + 9 q^{11} + 31 q^{12} + 18 q^{13} + 11 q^{14} + 25 q^{15} + 39 q^{16} - 8 q^{17} + 11 q^{18} + 11 q^{19}+ \cdots + 9 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.37846 1.00000 3.65709 1.00000 −2.37846 −2.06593 −3.94134 1.00000 −2.37846
1.2 −2.29641 1.00000 3.27349 1.00000 −2.29641 −2.28611 −2.92446 1.00000 −2.29641
1.3 −2.21783 1.00000 2.91878 1.00000 −2.21783 −1.19670 −2.03770 1.00000 −2.21783
1.4 −2.00202 1.00000 2.00810 1.00000 −2.00202 3.16837 −0.0162194 1.00000 −2.00202
1.5 −1.35850 1.00000 −0.154487 1.00000 −1.35850 1.13918 2.92686 1.00000 −1.35850
1.6 −1.21693 1.00000 −0.519082 1.00000 −1.21693 −3.32401 3.06555 1.00000 −1.21693
1.7 −1.17495 1.00000 −0.619503 1.00000 −1.17495 4.87740 3.07777 1.00000 −1.17495
1.8 −1.08036 1.00000 −0.832828 1.00000 −1.08036 2.50098 3.06047 1.00000 −1.08036
1.9 −0.404849 1.00000 −1.83610 1.00000 −0.404849 1.25801 1.55304 1.00000 −0.404849
1.10 −0.358480 1.00000 −1.87149 1.00000 −0.358480 −2.43554 1.38785 1.00000 −0.358480
1.11 0.117537 1.00000 −1.98618 1.00000 0.117537 −2.82367 −0.468525 1.00000 0.117537
1.12 0.134140 1.00000 −1.98201 1.00000 0.134140 1.40831 −0.534145 1.00000 0.134140
1.13 0.872240 1.00000 −1.23920 1.00000 0.872240 3.30692 −2.82536 1.00000 0.872240
1.14 0.940321 1.00000 −1.11580 1.00000 0.940321 0.900767 −2.92985 1.00000 0.940321
1.15 1.14392 1.00000 −0.691452 1.00000 1.14392 1.05238 −3.07880 1.00000 1.14392
1.16 1.40188 1.00000 −0.0347196 1.00000 1.40188 −5.24426 −2.85244 1.00000 1.40188
1.17 1.50967 1.00000 0.279113 1.00000 1.50967 2.29097 −2.59798 1.00000 1.50967
1.18 1.96315 1.00000 1.85395 1.00000 1.96315 4.65397 −0.286724 1.00000 1.96315
1.19 2.02762 1.00000 2.11124 1.00000 2.02762 3.74723 0.225557 1.00000 2.02762
1.20 2.03825 1.00000 2.15445 1.00000 2.03825 −3.70333 0.314810 1.00000 2.03825
See all 25 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( -1 \)
\(23\) \( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 7935.2.a.bw 25
23.b odd 2 1 7935.2.a.bv 25
23.d odd 22 2 345.2.m.c ✓ 50
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
345.2.m.c ✓ 50 23.d odd 22 2
7935.2.a.bv 25 23.b odd 2 1
7935.2.a.bw 25 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7935))\):

\( T_{2}^{25} - 11 T_{2}^{24} + 20 T_{2}^{23} + 198 T_{2}^{22} - 844 T_{2}^{21} - 836 T_{2}^{20} + \cdots - 253 \) Copy content Toggle raw display
\( T_{7}^{25} - 7 T_{7}^{24} - 83 T_{7}^{23} + 644 T_{7}^{22} + 2739 T_{7}^{21} - 24826 T_{7}^{20} + \cdots - 902144 \) Copy content Toggle raw display
\( T_{11}^{25} - 9 T_{11}^{24} - 126 T_{11}^{23} + 1329 T_{11}^{22} + 5698 T_{11}^{21} - 80067 T_{11}^{20} + \cdots - 106714112 \) Copy content Toggle raw display