# Properties

 Label 2151.4.a.c Level $2151$ Weight $4$ Character orbit 2151.a Self dual yes Analytic conductor $126.913$ Analytic rank $0$ Dimension $28$ CM no Inner twists $1$

# Related objects

## 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: $$28$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$28q + 13q^{2} + 99q^{4} + 74q^{5} - 82q^{7} + 135q^{8} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$28q + 13q^{2} + 99q^{4} + 74q^{5} - 82q^{7} + 135q^{8} - 68q^{10} + 258q^{11} - 134q^{13} + 292q^{14} + 327q^{16} + 364q^{17} - 278q^{19} + 986q^{20} - 179q^{22} + 668q^{23} + 490q^{25} + 760q^{26} - 802q^{28} + 714q^{29} - 608q^{31} + 918q^{32} - 228q^{34} + 934q^{35} - 1080q^{37} + 1395q^{38} - 563q^{40} + 1796q^{41} - 1934q^{43} + 3157q^{44} - 940q^{46} + 2032q^{47} + 762q^{49} + 1754q^{50} - 2328q^{52} + 1790q^{53} - 478q^{55} + 3557q^{56} - 2626q^{58} + 3622q^{59} + 324q^{61} + 796q^{62} + 2023q^{64} + 2200q^{65} - 2444q^{67} - 357q^{68} + 4305q^{70} + 1298q^{71} - 1368q^{73} - 813q^{74} + 1390q^{76} + 1408q^{77} - 1378q^{79} + 7684q^{80} + 9001q^{82} + 3524q^{83} + 60q^{85} + 2543q^{86} + 1749q^{88} + 7854q^{89} + 850q^{91} + 496q^{92} + 6634q^{94} + 3696q^{95} - 1746q^{97} + 4632q^{98} + O(q^{100})$$

## 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 −5.43685 0 21.5594 21.1888 0 −20.1660 −73.7203 0 −115.201
1.2 −4.27604 0 10.2845 1.46589 0 −24.3497 −9.76851 0 −6.26822
1.3 −4.23289 0 9.91739 1.28980 0 −27.4975 −8.11611 0 −5.45960
1.4 −4.04550 0 8.36609 10.3595 0 −12.7054 −1.48103 0 −41.9093
1.5 −3.82627 0 6.64037 6.06587 0 7.45896 5.20233 0 −23.2097
1.6 −3.21293 0 2.32292 13.8674 0 29.9628 18.2401 0 −44.5549
1.7 −3.00561 0 1.03369 −10.0458 0 −17.8583 20.9380 0 30.1936
1.8 −2.23264 0 −3.01532 −1.56125 0 −14.0459 24.5932 0 3.48572
1.9 −2.01135 0 −3.95446 6.74089 0 7.15060 24.0446 0 −13.5583
1.10 −1.55579 0 −5.57952 −17.3600 0 −1.16704 21.1269 0 27.0085
1.11 −0.686651 0 −7.52851 17.8875 0 15.8088 10.6627 0 −12.2825
1.12 −0.456628 0 −7.79149 −14.2736 0 −13.0550 7.21084 0 6.51773
1.13 −0.404541 0 −7.83635 0.184451 0 12.9030 6.40644 0 −0.0746179
1.14 0.608170 0 −7.63013 1.98658 0 −5.67520 −9.50578 0 1.20818
1.15 0.797577 0 −7.36387 7.16277 0 0.569206 −12.2539 0 5.71286
1.16 1.27488 0 −6.37468 17.5425 0 −26.4099 −18.3260 0 22.3646
1.17 1.64745 0 −5.28592 −5.57976 0 35.6078 −21.8878 0 −9.19235
1.18 2.03138 0 −3.87348 −11.5727 0 −13.0852 −24.1196 0 −23.5086
1.19 2.60026 0 −1.23865 11.0636 0 −16.8612 −24.0229 0 28.7682
1.20 3.06927 0 1.42044 −10.0975 0 1.48241 −20.1945 0 −30.9919
See all 28 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.28 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## 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.c 28
3.b odd 2 1 717.4.a.a 28

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
717.4.a.a 28 3.b odd 2 1
2151.4.a.c 28 1.a even 1 1 trivial