Properties

Label 6023.2.a.c
Level $6023$
Weight $2$
Character orbit 6023.a
Self dual yes
Analytic conductor $48.094$
Analytic rank $0$
Dimension $138$
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] = [6023,2,Mod(1,6023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6023, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6023.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6023 = 19 \cdot 317 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6023.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: \(48.0938971374\)
Analytic rank: \(0\)
Dimension: \(138\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 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 −2.80790 2.44752 5.88430 0.306657 −6.87238 −4.87771 −10.9067 2.99034 −0.861061
1.2 −2.76304 −0.570737 5.63440 2.36853 1.57697 1.21818 −10.0420 −2.67426 −6.54436
1.3 −2.74148 −0.0386597 5.51569 −1.76662 0.105985 3.31998 −9.63818 −2.99851 4.84315
1.4 −2.68395 2.15160 5.20359 1.49960 −5.77479 0.747166 −8.59827 1.62938 −4.02486
1.5 −2.67199 3.08563 5.13955 −4.31422 −8.24478 2.33147 −8.38886 6.52111 11.5276
1.6 −2.67164 −1.61720 5.13764 −4.16220 4.32056 −1.04033 −8.38264 −0.384677 11.1199
1.7 −2.58182 −0.634269 4.66582 2.08330 1.63757 3.68872 −6.88267 −2.59770 −5.37871
1.8 −2.57032 −2.26358 4.60652 −0.389233 5.81812 0.261062 −6.69959 2.12381 1.00045
1.9 −2.56824 −3.23259 4.59584 −2.23172 8.30205 3.00174 −6.66674 7.44963 5.73158
1.10 −2.53137 2.03677 4.40782 3.56698 −5.15582 −0.371412 −6.09508 1.14845 −9.02935
1.11 −2.51157 0.714819 4.30797 −1.12509 −1.79532 −0.994631 −5.79662 −2.48903 2.82573
1.12 −2.40954 1.37728 3.80590 −2.93809 −3.31862 −1.98041 −4.35139 −1.10309 7.07945
1.13 −2.39602 −1.69365 3.74091 −0.534671 4.05801 −0.0216661 −4.17126 −0.131565 1.28108
1.14 −2.39507 3.00458 3.73634 −1.01813 −7.19617 −4.72960 −4.15865 6.02752 2.43848
1.15 −2.33668 3.18243 3.46006 4.06905 −7.43630 5.05493 −3.41169 7.12783 −9.50807
1.16 −2.26801 0.709403 3.14388 −4.17389 −1.60894 3.35218 −2.59433 −2.49675 9.46643
1.17 −2.24651 −2.33680 3.04682 3.03120 5.24966 −0.990135 −2.35169 2.46065 −6.80962
1.18 −2.22566 −1.96365 2.95355 3.43373 4.37041 −3.81546 −2.12228 0.855918 −7.64232
1.19 −2.22132 1.60897 2.93428 0.172135 −3.57405 −2.94325 −2.07533 −0.411206 −0.382368
1.20 −2.14132 0.0864735 2.58523 2.84531 −0.185167 1.71112 −1.25317 −2.99252 −6.09271
See next 80 embeddings (of 138 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.138
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(19\) \(-1\)
\(317\) \(1\)

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 6023.2.a.c 138
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6023.2.a.c 138 1.a even 1 1 trivial