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Properties

Label 3017.2.a.d
Level $3017$
Weight $2$
Character orbit 3017.a
Self dual yes
Analytic conductor $24.091$
Analytic rank $0$
Dimension $48$
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] = [3017,2,Mod(1,3017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3017, 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("3017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3017 = 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3017.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: \(24.0908662898\)
Analytic rank: \(0\)
Dimension: \(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + q^{2} + 7 q^{3} + 49 q^{4} + 6 q^{5} + 9 q^{6} - 48 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + q^{2} + 7 q^{3} + 49 q^{4} + 6 q^{5} + 9 q^{6} - 48 q^{7} + 6 q^{8} + 37 q^{9} + 19 q^{10} - 4 q^{11} + 16 q^{12} + 30 q^{13} - q^{14} + 16 q^{15} + 47 q^{16} + 20 q^{17} + 19 q^{18} + 39 q^{19} + 27 q^{20} - 7 q^{21} + 17 q^{22} + 28 q^{23} + 34 q^{24} + 42 q^{25} - 3 q^{26} + 31 q^{27} - 49 q^{28} - 19 q^{29} + 20 q^{30} + 30 q^{31} + 8 q^{32} + 8 q^{33} + 19 q^{34} - 6 q^{35} + 22 q^{36} + 11 q^{37} + 35 q^{38} + 8 q^{39} + 53 q^{40} + q^{41} - 9 q^{42} + 66 q^{43} + 6 q^{44} + 13 q^{45} - 31 q^{46} + 38 q^{47} + 53 q^{48} + 48 q^{49} + 26 q^{50} - q^{51} + 101 q^{52} + 35 q^{54} + 116 q^{55} - 6 q^{56} - 12 q^{57} - 29 q^{58} + 5 q^{59} + 38 q^{60} + 29 q^{61} + 63 q^{62} - 37 q^{63} + 44 q^{64} - 6 q^{65} + 34 q^{66} + 65 q^{67} + 48 q^{68} + 30 q^{69} - 19 q^{70} - 2 q^{71} + 45 q^{72} + 49 q^{73} + 34 q^{74} + 73 q^{75} + 66 q^{76} + 4 q^{77} + 28 q^{78} + 105 q^{79} + 68 q^{80} + 4 q^{81} + 54 q^{82} + 73 q^{83} - 16 q^{84} - 2 q^{85} - 32 q^{86} + 117 q^{87} + 73 q^{88} + 24 q^{89} + 97 q^{90} - 30 q^{91} + 49 q^{92} + 10 q^{93} + 43 q^{94} + 39 q^{95} + 73 q^{96} + 44 q^{97} + q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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 −2.79813 −1.80235 5.82953 0.751313 5.04321 −1.00000 −10.7155 0.248469 −2.10227
1.2 −2.64760 0.213217 5.00978 −2.16055 −0.564512 −1.00000 −7.96868 −2.95454 5.72027
1.3 −2.56242 2.64363 4.56600 −3.58765 −6.77408 −1.00000 −6.57516 3.98876 9.19305
1.4 −2.45807 1.55172 4.04211 2.77317 −3.81423 −1.00000 −5.01964 −0.592173 −6.81664
1.5 −2.45480 1.18122 4.02605 2.34847 −2.89965 −1.00000 −4.97356 −1.60473 −5.76503
1.6 −2.28002 −2.12415 3.19849 −2.35991 4.84309 −1.00000 −2.73257 1.51199 5.38065
1.7 −2.17059 −2.57325 2.71147 1.16563 5.58547 −1.00000 −1.54430 3.62160 −2.53011
1.8 −1.86774 −1.75582 1.48847 1.04699 3.27943 −1.00000 0.955415 0.0829173 −1.95551
1.9 −1.83176 0.231975 1.35534 1.42216 −0.424922 −1.00000 1.18086 −2.94619 −2.60505
1.10 −1.77135 −0.901963 1.13767 0.320921 1.59769 −1.00000 1.52749 −2.18646 −0.568461
1.11 −1.74956 2.55237 1.06096 3.79184 −4.46552 −1.00000 1.64290 3.51459 −6.63405
1.12 −1.72910 2.06378 0.989799 −1.08979 −3.56848 −1.00000 1.74674 1.25918 1.88435
1.13 −1.62689 0.122820 0.646766 −1.80063 −0.199815 −1.00000 2.20156 −2.98492 2.92942
1.14 −1.50997 −2.55745 0.279999 −4.15223 3.86166 −1.00000 2.59714 3.54053 6.26973
1.15 −1.41996 0.0236660 0.0162806 3.58797 −0.0336048 −1.00000 2.81680 −2.99944 −5.09476
1.16 −1.20729 2.29968 −0.542443 −3.47701 −2.77639 −1.00000 3.06947 2.28854 4.19777
1.17 −1.11428 −2.03270 −0.758384 −1.43344 2.26500 −1.00000 3.07361 1.13188 1.59725
1.18 −0.994083 3.30586 −1.01180 0.477036 −3.28630 −1.00000 2.99398 7.92873 −0.474214
1.19 −0.545191 −0.363386 −1.70277 −2.08026 0.198114 −1.00000 2.01871 −2.86795 1.13414
1.20 −0.441935 −0.143023 −1.80469 3.37248 0.0632070 −1.00000 1.68143 −2.97954 −1.49042
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.48
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(1\)
\(431\) \(-1\)

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 3017.2.a.d ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3017.2.a.d ✓ 48 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{48} - T_{2}^{47} - 72 T_{2}^{46} + 69 T_{2}^{45} + 2414 T_{2}^{44} - 2210 T_{2}^{43} - 50072 T_{2}^{42} + \cdots + 115 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3017))\). Copy content Toggle raw display