Properties

Label 8012.2.a.a
Level 8012
Weight 2
Character orbit 8012.a
Self dual Yes
Analytic conductor 63.976
Analytic rank 1
Dimension 79
CM No

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Newspace parameters

Level: \( N \) = \( 8012 = 2^{2} \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9761420994\)
Analytic rank: \(1\)
Dimension: \(79\)
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.

\(\operatorname{Tr}(f)(q) = \) \(79q \) \(\mathstrut -\mathstrut 19q^{3} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(79q \) \(\mathstrut -\mathstrut 19q^{3} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut -\mathstrut 30q^{17} \) \(\mathstrut -\mathstrut 49q^{19} \) \(\mathstrut +\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 40q^{23} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 70q^{27} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 48q^{31} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut -\mathstrut 34q^{35} \) \(\mathstrut -\mathstrut 35q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 104q^{43} \) \(\mathstrut +\mathstrut 12q^{45} \) \(\mathstrut -\mathstrut 38q^{47} \) \(\mathstrut +\mathstrut 51q^{49} \) \(\mathstrut -\mathstrut 41q^{51} \) \(\mathstrut -\mathstrut q^{53} \) \(\mathstrut -\mathstrut 112q^{55} \) \(\mathstrut -\mathstrut 34q^{57} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 120q^{63} \) \(\mathstrut -\mathstrut 21q^{65} \) \(\mathstrut -\mathstrut 67q^{67} \) \(\mathstrut +\mathstrut 15q^{69} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 88q^{73} \) \(\mathstrut -\mathstrut 103q^{75} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 99q^{79} \) \(\mathstrut +\mathstrut 47q^{81} \) \(\mathstrut -\mathstrut 70q^{83} \) \(\mathstrut +\mathstrut 7q^{85} \) \(\mathstrut -\mathstrut 109q^{87} \) \(\mathstrut -\mathstrut 50q^{89} \) \(\mathstrut -\mathstrut 83q^{91} \) \(\mathstrut -\mathstrut 7q^{93} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 93q^{97} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.41908 0 −3.90530 0 −4.72288 0 8.69013 0
1.2 0 −3.40885 0 −1.83301 0 1.65667 0 8.62026 0
1.3 0 −3.26026 0 0.973052 0 −2.06988 0 7.62930 0
1.4 0 −3.24921 0 4.44468 0 −2.04361 0 7.55734 0
1.5 0 −3.22159 0 3.40512 0 −1.04725 0 7.37863 0
1.6 0 −3.17871 0 −1.27908 0 2.10162 0 7.10419 0
1.7 0 −3.11170 0 0.355389 0 −3.83214 0 6.68266 0
1.8 0 −2.87938 0 2.41591 0 2.96745 0 5.29083 0
1.9 0 −2.79728 0 3.00547 0 −2.16180 0 4.82477 0
1.10 0 −2.71048 0 −2.47152 0 2.42570 0 4.34670 0
1.11 0 −2.68647 0 −0.588575 0 −1.13984 0 4.21715 0
1.12 0 −2.62866 0 2.26034 0 −4.56855 0 3.90985 0
1.13 0 −2.59561 0 −1.81816 0 −1.23436 0 3.73718 0
1.14 0 −2.46774 0 −2.83803 0 1.20715 0 3.08972 0
1.15 0 −2.30440 0 3.02168 0 4.18657 0 2.31024 0
1.16 0 −2.27913 0 −0.601984 0 3.53846 0 2.19442 0
1.17 0 −2.21676 0 1.73805 0 −5.05782 0 1.91402 0
1.18 0 −2.02583 0 1.86007 0 1.58288 0 1.10398 0
1.19 0 −1.92727 0 −2.52260 0 −3.66775 0 0.714366 0
1.20 0 −1.87872 0 3.33381 0 1.62469 0 0.529574 0
See all 79 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.79
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(2003\) \(-1\)