Properties

 Label 8044.2.a.a Level 8044 Weight 2 Character orbit 8044.a Self dual Yes Analytic conductor 64.232 Analytic rank 1 Dimension 80 CM No

Related objects

Newspace parameters

 Level: $$N$$ = $$8044 = 2^{2} \cdot 2011$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 8044.a (trivial)

Newform invariants

 Self dual: Yes Analytic conductor: $$64.2316633859$$ Analytic rank: $$1$$ Dimension: $$80$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$80q$$ $$\mathstrut -\mathstrut 13q^{3}$$ $$\mathstrut -\mathstrut 2q^{5}$$ $$\mathstrut -\mathstrut 12q^{7}$$ $$\mathstrut +\mathstrut 63q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$80q$$ $$\mathstrut -\mathstrut 13q^{3}$$ $$\mathstrut -\mathstrut 2q^{5}$$ $$\mathstrut -\mathstrut 12q^{7}$$ $$\mathstrut +\mathstrut 63q^{9}$$ $$\mathstrut -\mathstrut 34q^{11}$$ $$\mathstrut -\mathstrut q^{13}$$ $$\mathstrut -\mathstrut 24q^{15}$$ $$\mathstrut -\mathstrut 35q^{17}$$ $$\mathstrut -\mathstrut 31q^{19}$$ $$\mathstrut -\mathstrut 3q^{21}$$ $$\mathstrut -\mathstrut 43q^{23}$$ $$\mathstrut +\mathstrut 58q^{25}$$ $$\mathstrut -\mathstrut 49q^{27}$$ $$\mathstrut -\mathstrut 5q^{29}$$ $$\mathstrut -\mathstrut 56q^{31}$$ $$\mathstrut -\mathstrut 23q^{33}$$ $$\mathstrut -\mathstrut 72q^{35}$$ $$\mathstrut -\mathstrut 11q^{37}$$ $$\mathstrut -\mathstrut 74q^{39}$$ $$\mathstrut -\mathstrut 81q^{41}$$ $$\mathstrut -\mathstrut 34q^{43}$$ $$\mathstrut -\mathstrut 14q^{45}$$ $$\mathstrut -\mathstrut 64q^{47}$$ $$\mathstrut +\mathstrut 40q^{49}$$ $$\mathstrut -\mathstrut 59q^{51}$$ $$\mathstrut +\mathstrut 3q^{53}$$ $$\mathstrut -\mathstrut 53q^{55}$$ $$\mathstrut -\mathstrut 34q^{57}$$ $$\mathstrut -\mathstrut 116q^{59}$$ $$\mathstrut -\mathstrut 13q^{61}$$ $$\mathstrut -\mathstrut 61q^{63}$$ $$\mathstrut -\mathstrut 55q^{65}$$ $$\mathstrut -\mathstrut 22q^{67}$$ $$\mathstrut -\mathstrut 10q^{69}$$ $$\mathstrut -\mathstrut 86q^{71}$$ $$\mathstrut -\mathstrut 32q^{73}$$ $$\mathstrut -\mathstrut 85q^{75}$$ $$\mathstrut +\mathstrut 4q^{77}$$ $$\mathstrut -\mathstrut 88q^{79}$$ $$\mathstrut +\mathstrut 12q^{81}$$ $$\mathstrut -\mathstrut 83q^{83}$$ $$\mathstrut -\mathstrut 2q^{85}$$ $$\mathstrut -\mathstrut 87q^{87}$$ $$\mathstrut -\mathstrut 72q^{89}$$ $$\mathstrut -\mathstrut 49q^{91}$$ $$\mathstrut -\mathstrut 102q^{95}$$ $$\mathstrut -\mathstrut 34q^{97}$$ $$\mathstrut -\mathstrut 103q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

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 0 −3.40275 0 −1.72550 0 −2.88747 0 8.57873 0
1.2 0 −3.30826 0 0.889537 0 −1.31364 0 7.94459 0
1.3 0 −3.15920 0 −3.92220 0 2.93790 0 6.98053 0
1.4 0 −3.15577 0 3.07374 0 −1.51261 0 6.95887 0
1.5 0 −3.13382 0 2.56113 0 −0.308664 0 6.82084 0
1.6 0 −3.01017 0 −0.450076 0 4.39052 0 6.06114 0
1.7 0 −2.88063 0 4.02746 0 2.18923 0 5.29800 0
1.8 0 −2.78192 0 1.93177 0 −4.05350 0 4.73908 0
1.9 0 −2.69065 0 −1.88521 0 −0.388125 0 4.23960 0
1.10 0 −2.64514 0 −1.03664 0 1.03871 0 3.99678 0
1.11 0 −2.64034 0 1.50045 0 0.628661 0 3.97141 0
1.12 0 −2.57629 0 −1.13453 0 −4.92532 0 3.63726 0
1.13 0 −2.57058 0 3.02835 0 −3.19846 0 3.60789 0
1.14 0 −2.56684 0 −2.59165 0 1.04792 0 3.58865 0
1.15 0 −2.41417 0 −0.367373 0 2.85158 0 2.82820 0
1.16 0 −2.27117 0 −3.46385 0 −0.730522 0 2.15820 0
1.17 0 −2.04584 0 −1.96310 0 −5.24497 0 1.18544 0
1.18 0 −1.94593 0 4.46459 0 −3.96440 0 0.786636 0
1.19 0 −1.93385 0 −1.81561 0 3.06905 0 0.739771 0
1.20 0 −1.85715 0 0.680485 0 2.30245 0 0.448994 0
See all 80 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.80 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$-1$$
$$2011$$ $$-1$$