Properties

Label 2151.4.a.d
Level $2151$
Weight $4$
Character orbit 2151.a
Self dual yes
Analytic conductor $126.913$
Analytic rank $1$
Dimension $32$
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: \(1\)
Dimension: \(32\)
Twist minimal: no (minimal twist has level 717)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32q - 11q^{2} + 147q^{4} - 66q^{5} + 58q^{7} - 153q^{8} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 32q - 11q^{2} + 147q^{4} - 66q^{5} + 58q^{7} - 153q^{8} + 52q^{10} - 270q^{11} + 48q^{13} - 184q^{14} + 775q^{16} - 384q^{17} + 216q^{19} - 534q^{20} + 437q^{22} - 712q^{23} + 1190q^{25} - 436q^{26} + 598q^{28} - 562q^{29} + 384q^{31} - 1770q^{32} + 452q^{34} - 1026q^{35} + 770q^{37} - 733q^{38} + 877q^{40} - 1648q^{41} + 1592q^{43} - 1595q^{44} + 532q^{46} - 1540q^{47} + 2134q^{49} - 1646q^{50} - 144q^{52} - 1708q^{53} + 1282q^{55} - 2155q^{56} + 1086q^{58} - 2396q^{59} + 364q^{61} - 2180q^{62} + 1663q^{64} - 1520q^{65} + 2728q^{67} - 1545q^{68} - 4609q^{70} - 3322q^{71} - 188q^{73} - 1111q^{74} - 3134q^{76} - 556q^{77} - 462q^{79} - 6076q^{80} - 7965q^{82} - 4604q^{83} - 852q^{85} - 549q^{86} - 1127q^{88} - 6742q^{89} + 1390q^{91} - 1802q^{92} - 2796q^{94} - 448q^{95} - 1322q^{97} - 1000q^{98} + O(q^{100}) \)

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 −5.59453 0 23.2988 −16.4914 0 −10.5009 −85.5894 0 92.2616
1.2 −5.31397 0 20.2383 −1.11401 0 6.72325 −65.0342 0 5.91984
1.3 −5.23366 0 19.3912 13.4597 0 28.9382 −59.6177 0 −70.4436
1.4 −5.16397 0 18.6666 0.429463 0 −25.9056 −55.0823 0 −2.21774
1.5 −4.76460 0 14.7014 −12.2551 0 22.9067 −31.9296 0 58.3909
1.6 −4.73063 0 14.3788 −2.38638 0 21.4748 −30.1758 0 11.2891
1.7 −4.24177 0 9.99259 −19.4944 0 −4.35055 −8.45209 0 82.6908
1.8 −3.87098 0 6.98450 17.8390 0 4.77620 3.93099 0 −69.0545
1.9 −3.63855 0 5.23901 −13.7159 0 7.38539 10.0460 0 49.9058
1.10 −2.74193 0 −0.481825 19.5291 0 −9.73710 23.2566 0 −53.5474
1.11 −2.35922 0 −2.43409 −3.14815 0 −17.8040 24.6163 0 7.42716
1.12 −2.25922 0 −2.89594 −14.4181 0 23.8295 24.6163 0 32.5737
1.13 −2.06669 0 −3.72878 0.727240 0 31.6777 24.2398 0 −1.50298
1.14 −1.28682 0 −6.34409 14.8834 0 −31.0382 18.4583 0 −19.1522
1.15 −1.10380 0 −6.78162 −20.8736 0 −33.6250 16.3160 0 23.0403
1.16 −0.980358 0 −7.03890 13.2849 0 4.25684 14.7435 0 −13.0240
1.17 −0.197960 0 −7.96081 0.664309 0 12.2133 3.15960 0 −0.131506
1.18 0.323742 0 −7.89519 −13.7872 0 10.6908 −5.14594 0 −4.46348
1.19 0.560231 0 −7.68614 −18.3687 0 31.3786 −8.78786 0 −10.2907
1.20 0.752561 0 −7.43365 −3.00130 0 −33.6762 −11.6148 0 −2.25866
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.32
Significant digits:
Format:

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.d 32
3.b odd 2 1 717.4.a.d 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
717.4.a.d 32 3.b odd 2 1
2151.4.a.d 32 1.a even 1 1 trivial