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Properties

Label 7105.2.a.bg
Level $7105$
Weight $2$
Character orbit 7105.a
Self dual yes
Analytic conductor $56.734$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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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] = [7105,2,Mod(1,7105)] 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("7105.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7105, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 7105 = 5 \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7105.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [21,6,7,24,21] 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: yes
Analytic conductor: \(56.7337106361\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 1015)
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.

\(\operatorname{Tr}(f)(q) = \) \( 21 q + 6 q^{2} + 7 q^{3} + 24 q^{4} + 21 q^{5} + 21 q^{8} + 28 q^{9} + 6 q^{10} + 19 q^{11} + 16 q^{12} + 7 q^{13} + 7 q^{15} + 30 q^{16} + 10 q^{17} + 29 q^{18} - 5 q^{19} + 24 q^{20} + q^{22} + 21 q^{23}+ \cdots + 48 q^{99}+O(q^{100}) \) 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 −2.54462 1.64978 4.47507 1.00000 −4.19805 0 −6.29811 −0.278232 −2.54462
1.2 −2.34587 −0.535420 3.50310 1.00000 1.25602 0 −3.52606 −2.71333 −2.34587
1.3 −2.00669 3.21029 2.02680 1.00000 −6.44205 0 −0.0537772 7.30594 −2.00669
1.4 −1.82702 −2.84881 1.33802 1.00000 5.20485 0 1.20946 5.11575 −1.82702
1.5 −1.56583 1.27952 0.451829 1.00000 −2.00352 0 2.42418 −1.36282 −1.56583
1.6 −1.18586 −1.25268 −0.593725 1.00000 1.48550 0 3.07581 −1.43080 −1.18586
1.7 −1.09895 1.28957 −0.792311 1.00000 −1.41718 0 3.06861 −1.33700 −1.09895
1.8 −0.385974 −0.792276 −1.85102 1.00000 0.305797 0 1.48639 −2.37230 −0.385974
1.9 −0.362896 2.98487 −1.86831 1.00000 −1.08319 0 1.40379 5.90942 −0.362896
1.10 −0.249528 −1.05869 −1.93774 1.00000 0.264173 0 0.982576 −1.87917 −0.249528
1.11 0.547287 −1.96374 −1.70048 1.00000 −1.07473 0 −2.02522 0.856290 0.547287
1.12 0.776571 1.66747 −1.39694 1.00000 1.29491 0 −2.63796 −0.219530 0.776571
1.13 1.05882 3.30833 −0.878907 1.00000 3.50291 0 −3.04823 7.94504 1.05882
1.14 1.43949 −0.844489 0.0721453 1.00000 −1.21564 0 −2.77514 −2.28684 1.43949
1.15 1.45784 0.625640 0.125292 1.00000 0.912082 0 −2.73302 −2.60857 1.45784
1.16 1.56070 −2.95493 0.435785 1.00000 −4.61177 0 −2.44127 5.73163 1.56070
1.17 2.20420 2.19053 2.85851 1.00000 4.82837 0 1.89233 1.79842 2.20420
1.18 2.56067 1.67307 4.55704 1.00000 4.28418 0 6.54775 −0.200836 2.56067
1.19 2.57459 −0.879880 4.62849 1.00000 −2.26533 0 6.76729 −2.22581 2.57459
1.20 2.64792 −2.89244 5.01146 1.00000 −7.65893 0 7.97409 5.36619 2.64792
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \( -1 \)
\(7\) \( -1 \)
\(29\) \( -1 \)

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 7105.2.a.bg 21
7.b odd 2 1 7105.2.a.bf 21
7.d odd 6 2 1015.2.i.e ✓ 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1015.2.i.e ✓ 42 7.d odd 6 2
7105.2.a.bf 21 7.b odd 2 1
7105.2.a.bg 21 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7105))\):

\( T_{2}^{21} - 6 T_{2}^{20} - 15 T_{2}^{19} + 147 T_{2}^{18} + 9 T_{2}^{17} - 1474 T_{2}^{16} + 1126 T_{2}^{15} + \cdots - 243 \) Copy content Toggle raw display
\( T_{3}^{21} - 7 T_{3}^{20} - 21 T_{3}^{19} + 238 T_{3}^{18} + 12 T_{3}^{17} - 3238 T_{3}^{16} + \cdots - 20736 \) Copy content Toggle raw display
\( T_{17}^{21} - 10 T_{17}^{20} - 116 T_{17}^{19} + 1257 T_{17}^{18} + 5263 T_{17}^{17} - 62511 T_{17}^{16} + \cdots + 1206549 \) Copy content Toggle raw display