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Properties

Label 2151.4.a.h
Level $2151$
Weight $4$
Character orbit 2151.a
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $59$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(126.913108422\)
Analytic rank: \(0\)
Dimension: \(59\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.26507 0 19.7210 20.1774 0 −13.2314 −61.7120 0 −106.236
1.2 −5.24697 0 19.5307 10.0958 0 0.804440 −60.5014 0 −52.9726
1.3 −5.15423 0 18.5661 1.27174 0 −23.0732 −54.4599 0 −6.55481
1.4 −5.11618 0 18.1753 6.15957 0 24.2123 −52.0584 0 −31.5134
1.5 −5.09369 0 17.9457 −15.2658 0 −21.0984 −50.6602 0 77.7594
1.6 −4.50896 0 12.3307 −9.52144 0 −13.3640 −19.5269 0 42.9318
1.7 −4.45221 0 11.8222 12.0796 0 −15.4984 −17.0170 0 −53.7808
1.8 −4.45149 0 11.8157 14.0297 0 23.7055 −16.9858 0 −62.4530
1.9 −4.40394 0 11.3946 1.03938 0 0.641944 −14.9498 0 −4.57738
1.10 −4.10283 0 8.83322 −7.42154 0 5.67497 −3.41855 0 30.4493
1.11 −3.99709 0 7.97675 −4.04840 0 −1.10463 0.0929295 0 16.1818
1.12 −3.78499 0 6.32612 −5.39134 0 9.96233 6.33562 0 20.4061
1.13 −3.13470 0 1.82636 −4.91209 0 36.3874 19.3525 0 15.3979
1.14 −3.10672 0 1.65170 −17.8784 0 0.745718 19.7224 0 55.5430
1.15 −2.96448 0 0.788155 20.3046 0 −25.7042 21.3794 0 −60.1925
1.16 −2.96328 0 0.781040 9.17370 0 2.35613 21.3918 0 −27.1843
1.17 −2.95118 0 0.709472 −16.6350 0 −30.2397 21.5157 0 49.0928
1.18 −2.78319 0 −0.253830 19.2360 0 27.5534 22.9720 0 −53.5375
1.19 −2.12161 0 −3.49876 4.52878 0 14.7886 24.3959 0 −9.60831
1.20 −1.92673 0 −4.28770 −4.54299 0 −14.1149 23.6751 0 8.75313
See all 59 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.59
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(239\) \(1\)

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 2151.4.a.h yes 59
3.b odd 2 1 2151.4.a.g ✓ 59
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2151.4.a.g ✓ 59 3.b odd 2 1
2151.4.a.h yes 59 1.a even 1 1 trivial