Properties

Label 8012.2.a.b
Level 8012
Weight 2
Character orbit 8012.a
Self dual Yes
Analytic conductor 63.976
Analytic rank 0
Dimension 88
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: \(0\)
Dimension: \(88\)
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.

\(\operatorname{Tr}(f)(q) = \) \(88q \) \(\mathstrut +\mathstrut 19q^{3} \) \(\mathstrut +\mathstrut 44q^{7} \) \(\mathstrut +\mathstrut 99q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(88q \) \(\mathstrut +\mathstrut 19q^{3} \) \(\mathstrut +\mathstrut 44q^{7} \) \(\mathstrut +\mathstrut 99q^{9} \) \(\mathstrut +\mathstrut 16q^{11} \) \(\mathstrut -\mathstrut 3q^{13} \) \(\mathstrut +\mathstrut 21q^{15} \) \(\mathstrut +\mathstrut 32q^{17} \) \(\mathstrut +\mathstrut 49q^{19} \) \(\mathstrut +\mathstrut 7q^{21} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 114q^{25} \) \(\mathstrut +\mathstrut 82q^{27} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 31q^{33} \) \(\mathstrut +\mathstrut 26q^{35} \) \(\mathstrut +\mathstrut 37q^{39} \) \(\mathstrut +\mathstrut 22q^{41} \) \(\mathstrut +\mathstrut 98q^{43} \) \(\mathstrut +\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 48q^{47} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut +\mathstrut 55q^{51} \) \(\mathstrut -\mathstrut q^{53} \) \(\mathstrut +\mathstrut 116q^{55} \) \(\mathstrut +\mathstrut 62q^{57} \) \(\mathstrut +\mathstrut 34q^{59} \) \(\mathstrut +\mathstrut 132q^{63} \) \(\mathstrut +\mathstrut 39q^{65} \) \(\mathstrut +\mathstrut 75q^{67} \) \(\mathstrut +\mathstrut 15q^{69} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut 104q^{73} \) \(\mathstrut +\mathstrut 87q^{75} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 111q^{79} \) \(\mathstrut +\mathstrut 128q^{81} \) \(\mathstrut +\mathstrut 64q^{83} \) \(\mathstrut +\mathstrut 7q^{85} \) \(\mathstrut +\mathstrut 115q^{87} \) \(\mathstrut +\mathstrut 14q^{89} \) \(\mathstrut +\mathstrut 73q^{91} \) \(\mathstrut -\mathstrut 7q^{93} \) \(\mathstrut +\mathstrut 51q^{95} \) \(\mathstrut +\mathstrut 117q^{97} \) \(\mathstrut +\mathstrut 72q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.23075 0 0.167791 0 3.73844 0 7.43772 0
1.2 0 −3.15616 0 −3.31880 0 0.188587 0 6.96136 0
1.3 0 −3.04318 0 2.19188 0 3.84643 0 6.26097 0
1.4 0 −2.94029 0 −0.651594 0 3.16105 0 5.64533 0
1.5 0 −2.81005 0 4.18979 0 3.58597 0 4.89636 0
1.6 0 −2.80891 0 −0.455894 0 −2.00885 0 4.88996 0
1.7 0 −2.80739 0 2.13337 0 −1.30534 0 4.88143 0
1.8 0 −2.71734 0 −0.520933 0 −1.18624 0 4.38393 0
1.9 0 −2.71377 0 −3.80725 0 4.98615 0 4.36453 0
1.10 0 −2.59974 0 −0.601241 0 −1.05390 0 3.75864 0
1.11 0 −2.56711 0 −4.07865 0 0.492202 0 3.59005 0
1.12 0 −2.52878 0 2.30231 0 0.0873376 0 3.39472 0
1.13 0 −2.48630 0 −2.95359 0 −3.19667 0 3.18170 0
1.14 0 −2.24743 0 −3.82088 0 −1.51483 0 2.05096 0
1.15 0 −2.08516 0 1.63979 0 1.21456 0 1.34791 0
1.16 0 −2.06140 0 1.88031 0 −1.75026 0 1.24936 0
1.17 0 −2.04818 0 1.65769 0 −0.109887 0 1.19506 0
1.18 0 −1.98040 0 1.50325 0 0.615748 0 0.921997 0
1.19 0 −1.83871 0 −1.10593 0 4.51431 0 0.380865 0
1.20 0 −1.72366 0 3.80404 0 −2.57590 0 −0.0289913 0
See all 88 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.88
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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