Properties

Label 6035.2.a.d
Level $6035$
Weight $2$
Character orbit 6035.a
Self dual yes
Analytic conductor $48.190$
Analytic rank $1$
Dimension $44$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6035,2,Mod(1,6035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6035, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6035.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6035 = 5 \cdot 17 \cdot 71 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6035.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.1897176198\)
Analytic rank: \(1\)
Dimension: \(44\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 2 q^{2} - 8 q^{3} + 38 q^{4} - 44 q^{5} - 10 q^{6} - 13 q^{7} - 6 q^{8} + 46 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q - 2 q^{2} - 8 q^{3} + 38 q^{4} - 44 q^{5} - 10 q^{6} - 13 q^{7} - 6 q^{8} + 46 q^{9} + 2 q^{10} - 4 q^{11} - 22 q^{12} - 19 q^{13} + 8 q^{15} + 22 q^{16} + 44 q^{17} - 3 q^{18} - 15 q^{19} - 38 q^{20} - 9 q^{21} - 31 q^{22} - 38 q^{23} - 29 q^{24} + 44 q^{25} + 20 q^{26} - 35 q^{27} - 36 q^{28} - 24 q^{29} + 10 q^{30} - 3 q^{31} - 19 q^{32} - 17 q^{33} - 2 q^{34} + 13 q^{35} + 24 q^{36} - 74 q^{37} - 15 q^{38} - 10 q^{39} + 6 q^{40} + 9 q^{41} - 12 q^{42} - 11 q^{43} + 11 q^{44} - 46 q^{45} - 30 q^{46} - 12 q^{47} - 30 q^{48} + 19 q^{49} - 2 q^{50} - 8 q^{51} - 21 q^{52} - 33 q^{53} + 12 q^{54} + 4 q^{55} + 3 q^{56} - 8 q^{57} - 38 q^{58} - 8 q^{59} + 22 q^{60} - 87 q^{61} - 47 q^{62} - 42 q^{63} + 12 q^{64} + 19 q^{65} - 13 q^{66} - 29 q^{67} + 38 q^{68} - 61 q^{69} + 44 q^{71} - 2 q^{72} - 39 q^{73} - 7 q^{74} - 8 q^{75} - 36 q^{76} - 45 q^{77} - 24 q^{78} - 25 q^{79} - 22 q^{80} + 52 q^{81} - 39 q^{82} - 12 q^{83} + 50 q^{84} - 44 q^{85} + 35 q^{86} - 4 q^{87} - 69 q^{88} + 56 q^{89} + 3 q^{90} - 21 q^{91} - 18 q^{92} - 32 q^{93} - 26 q^{94} + 15 q^{95} - 75 q^{96} - 80 q^{97} - 48 q^{98} - 25 q^{99}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.70980 −1.97129 5.34301 −1.00000 5.34180 −3.23556 −9.05887 0.885985 2.70980
1.2 −2.65545 0.992184 5.05140 −1.00000 −2.63469 2.21189 −8.10282 −2.01557 2.65545
1.3 −2.58454 0.349560 4.67987 −1.00000 −0.903452 −2.04775 −6.92624 −2.87781 2.58454
1.4 −2.43809 2.70086 3.94428 −1.00000 −6.58493 −4.52426 −4.74032 4.29464 2.43809
1.5 −2.35000 1.53391 3.52249 −1.00000 −3.60469 3.64205 −3.57785 −0.647109 2.35000
1.6 −2.32691 −2.96703 3.41452 −1.00000 6.90401 1.40727 −3.29145 5.80324 2.32691
1.7 −2.01551 2.29705 2.06228 −1.00000 −4.62973 2.65647 −0.125520 2.27646 2.01551
1.8 −1.90874 −1.84827 1.64328 −1.00000 3.52785 −4.00780 0.680888 0.416086 1.90874
1.9 −1.83345 −1.98397 1.36153 −1.00000 3.63750 3.16158 1.17060 0.936121 1.83345
1.10 −1.82282 −3.34912 1.32269 −1.00000 6.10486 −3.68631 1.23462 8.21664 1.82282
1.11 −1.63791 2.24378 0.682749 −1.00000 −3.67512 −2.25515 2.15754 2.03457 1.63791
1.12 −1.60438 −0.0375345 0.574038 −1.00000 0.0602197 0.265901 2.28779 −2.99859 1.60438
1.13 −1.46835 −1.29566 0.156056 −1.00000 1.90248 2.74106 2.70756 −1.32128 1.46835
1.14 −1.35784 0.0329488 −0.156280 −1.00000 −0.0447392 −2.89786 2.92788 −2.99891 1.35784
1.15 −1.09248 1.17404 −0.806486 −1.00000 −1.28261 −2.18845 3.06603 −1.62164 1.09248
1.16 −0.962995 1.93597 −1.07264 −1.00000 −1.86433 −0.00468227 2.95894 0.747980 0.962995
1.17 −0.731776 −2.99784 −1.46450 −1.00000 2.19375 0.653628 2.53524 5.98707 0.731776
1.18 −0.668824 1.88540 −1.55267 −1.00000 −1.26100 1.98654 2.37611 0.554720 0.668824
1.19 −0.546289 −0.826758 −1.70157 −1.00000 0.451649 2.37358 2.02213 −2.31647 0.546289
1.20 −0.529049 3.17925 −1.72011 −1.00000 −1.68198 −0.889199 1.96812 7.10763 0.529049
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.44
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(17\) \(-1\)
\(71\) \(-1\)

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 6035.2.a.d 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6035.2.a.d 44 1.a even 1 1 trivial