Properties

Label 2151.4.a.e
Level $2151$
Weight $4$
Character orbit 2151.a
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
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: \(0\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32q - 3q^{2} + 151q^{4} + 14q^{5} + 72q^{7} - 57q^{8} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 32q - 3q^{2} + 151q^{4} + 14q^{5} + 72q^{7} - 57q^{8} + 32q^{10} - 154q^{11} + 100q^{13} - 42q^{14} + 719q^{16} - 32q^{17} + 202q^{19} + 132q^{20} + 265q^{22} - 552q^{23} + 1086q^{25} + 280q^{26} + 390q^{28} + 154q^{29} + 560q^{31} - 444q^{32} + 156q^{34} - 394q^{35} + 914q^{37} - 111q^{38} + 257q^{40} + 914q^{41} + 1722q^{43} - 1243q^{44} + 584q^{46} - 380q^{47} + 2446q^{49} + 454q^{50} + 1552q^{52} - 370q^{53} + 918q^{55} + 499q^{56} + 2446q^{58} - 492q^{59} + 668q^{61} - 578q^{62} + 6475q^{64} - 736q^{65} + 4548q^{67} - 5253q^{68} + 7793q^{70} - 258q^{71} + 3096q^{73} - 449q^{74} + 6814q^{76} - 3804q^{77} + 2864q^{79} + 1052q^{80} + 14145q^{82} - 2364q^{83} + 3088q^{85} - 2811q^{86} + 8329q^{88} + 4172q^{89} + 7350q^{91} - 13644q^{92} + 6122q^{94} - 3336q^{95} + 6370q^{97} - 1572q^{98} + O(q^{100}) \)

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 −5.57745 0 23.1079 14.3698 0 −15.9726 −84.2636 0 −80.1465
1.2 −5.39980 0 21.1579 −14.7032 0 4.43362 −71.0498 0 79.3942
1.3 −5.21943 0 19.2424 −9.35484 0 26.3957 −58.6789 0 48.8269
1.4 −4.79937 0 15.0339 −7.96880 0 −5.93046 −33.7584 0 38.2452
1.5 −4.78487 0 14.8950 19.8446 0 9.72473 −32.9917 0 −94.9538
1.6 −4.32883 0 10.7387 −4.62088 0 32.0311 −11.8555 0 20.0030
1.7 −3.63451 0 5.20968 10.2507 0 −27.1739 10.1415 0 −37.2563
1.8 −3.11857 0 1.72551 0.660207 0 −24.6492 19.5675 0 −2.05890
1.9 −3.00815 0 1.04896 20.8509 0 −18.7019 20.9098 0 −62.7226
1.10 −2.96284 0 0.778438 −20.0660 0 −4.37640 21.3964 0 59.4524
1.11 −2.61906 0 −1.14052 −18.9589 0 25.2785 23.9396 0 49.6544
1.12 −2.35723 0 −2.44345 8.17039 0 34.4525 24.6177 0 −19.2595
1.13 −2.35460 0 −2.45587 5.04318 0 7.28879 24.6194 0 −11.8747
1.14 −1.44213 0 −5.92026 4.95653 0 −22.8735 20.0748 0 −7.14796
1.15 −0.568479 0 −7.67683 −0.988402 0 −12.3996 8.91196 0 0.561886
1.16 0.0917574 0 −7.99158 −10.9396 0 −5.88604 −1.46735 0 −1.00379
1.17 0.319477 0 −7.89793 −10.3242 0 16.6816 −5.07903 0 −3.29834
1.18 0.646340 0 −7.58224 13.9777 0 32.2049 −10.0714 0 9.03432
1.19 0.770960 0 −7.40562 −6.93927 0 33.2057 −11.8771 0 −5.34989
1.20 1.64226 0 −5.30297 14.9594 0 8.99120 −21.8470 0 24.5672
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.e 32
3.b odd 2 1 717.4.a.c 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
717.4.a.c 32 3.b odd 2 1
2151.4.a.e 32 1.a even 1 1 trivial