Properties

Label 8026.2.a.d
Level 8026
Weight 2
Character orbit 8026.a
Self dual Yes
Analytic conductor 64.088
Analytic rank 0
Dimension 96
CM No

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Newspace parameters

Level: \( N \) = \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0879326623\)
Analytic rank: \(0\)
Dimension: \(96\)
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.

\(\operatorname{Tr}(f)(q) = \) \(96q \) \(\mathstrut +\mathstrut 96q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 96q^{4} \) \(\mathstrut +\mathstrut 39q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 96q^{8} \) \(\mathstrut +\mathstrut 130q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(96q \) \(\mathstrut +\mathstrut 96q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 96q^{4} \) \(\mathstrut +\mathstrut 39q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 96q^{8} \) \(\mathstrut +\mathstrut 130q^{9} \) \(\mathstrut +\mathstrut 39q^{10} \) \(\mathstrut +\mathstrut 36q^{11} \) \(\mathstrut +\mathstrut 8q^{12} \) \(\mathstrut +\mathstrut 63q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 96q^{16} \) \(\mathstrut +\mathstrut 56q^{17} \) \(\mathstrut +\mathstrut 130q^{18} \) \(\mathstrut +\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 39q^{20} \) \(\mathstrut +\mathstrut 51q^{21} \) \(\mathstrut +\mathstrut 36q^{22} \) \(\mathstrut +\mathstrut 47q^{23} \) \(\mathstrut +\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 147q^{25} \) \(\mathstrut +\mathstrut 63q^{26} \) \(\mathstrut +\mathstrut 17q^{27} \) \(\mathstrut +\mathstrut 19q^{28} \) \(\mathstrut +\mathstrut 60q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 63q^{31} \) \(\mathstrut +\mathstrut 96q^{32} \) \(\mathstrut +\mathstrut 55q^{33} \) \(\mathstrut +\mathstrut 56q^{34} \) \(\mathstrut +\mathstrut 45q^{35} \) \(\mathstrut +\mathstrut 130q^{36} \) \(\mathstrut +\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 17q^{38} \) \(\mathstrut +\mathstrut 22q^{39} \) \(\mathstrut +\mathstrut 39q^{40} \) \(\mathstrut +\mathstrut 101q^{41} \) \(\mathstrut +\mathstrut 51q^{42} \) \(\mathstrut -\mathstrut 3q^{43} \) \(\mathstrut +\mathstrut 36q^{44} \) \(\mathstrut +\mathstrut 106q^{45} \) \(\mathstrut +\mathstrut 47q^{46} \) \(\mathstrut +\mathstrut 99q^{47} \) \(\mathstrut +\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut 175q^{49} \) \(\mathstrut +\mathstrut 147q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 63q^{52} \) \(\mathstrut +\mathstrut 75q^{53} \) \(\mathstrut +\mathstrut 17q^{54} \) \(\mathstrut +\mathstrut 80q^{55} \) \(\mathstrut +\mathstrut 19q^{56} \) \(\mathstrut +\mathstrut 35q^{57} \) \(\mathstrut +\mathstrut 60q^{58} \) \(\mathstrut +\mathstrut 129q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 75q^{61} \) \(\mathstrut +\mathstrut 63q^{62} \) \(\mathstrut +\mathstrut 20q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 55q^{65} \) \(\mathstrut +\mathstrut 55q^{66} \) \(\mathstrut +\mathstrut 2q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut +\mathstrut 57q^{69} \) \(\mathstrut +\mathstrut 45q^{70} \) \(\mathstrut +\mathstrut 87q^{71} \) \(\mathstrut +\mathstrut 130q^{72} \) \(\mathstrut +\mathstrut 120q^{73} \) \(\mathstrut +\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut +\mathstrut 17q^{76} \) \(\mathstrut +\mathstrut 95q^{77} \) \(\mathstrut +\mathstrut 22q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut 180q^{81} \) \(\mathstrut +\mathstrut 101q^{82} \) \(\mathstrut +\mathstrut 69q^{83} \) \(\mathstrut +\mathstrut 51q^{84} \) \(\mathstrut +\mathstrut 59q^{85} \) \(\mathstrut -\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 63q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 144q^{89} \) \(\mathstrut +\mathstrut 106q^{90} \) \(\mathstrut -\mathstrut 5q^{91} \) \(\mathstrut +\mathstrut 47q^{92} \) \(\mathstrut +\mathstrut 59q^{93} \) \(\mathstrut +\mathstrut 99q^{94} \) \(\mathstrut +\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 8q^{96} \) \(\mathstrut +\mathstrut 99q^{97} \) \(\mathstrut +\mathstrut 175q^{98} \) \(\mathstrut +\mathstrut 42q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 1.00000 −3.38260 1.00000 3.86577 −3.38260 1.67092 1.00000 8.44195 3.86577
1.2 1.00000 −3.34006 1.00000 0.570499 −3.34006 −3.09347 1.00000 8.15597 0.570499
1.3 1.00000 −3.28199 1.00000 4.44756 −3.28199 −4.87209 1.00000 7.77147 4.44756
1.4 1.00000 −3.27254 1.00000 −0.667760 −3.27254 −3.79895 1.00000 7.70950 −0.667760
1.5 1.00000 −3.25028 1.00000 −3.55308 −3.25028 1.03732 1.00000 7.56432 −3.55308
1.6 1.00000 −3.15603 1.00000 0.126707 −3.15603 5.16404 1.00000 6.96052 0.126707
1.7 1.00000 −2.94262 1.00000 −2.75708 −2.94262 −0.162948 1.00000 5.65901 −2.75708
1.8 1.00000 −2.86733 1.00000 −3.62078 −2.86733 −3.60760 1.00000 5.22157 −3.62078
1.9 1.00000 −2.84755 1.00000 2.66905 −2.84755 0.0156637 1.00000 5.10852 2.66905
1.10 1.00000 −2.83728 1.00000 3.92961 −2.83728 4.49024 1.00000 5.05014 3.92961
1.11 1.00000 −2.81326 1.00000 −0.734328 −2.81326 −3.92682 1.00000 4.91446 −0.734328
1.12 1.00000 −2.75991 1.00000 1.94869 −2.75991 −1.07781 1.00000 4.61711 1.94869
1.13 1.00000 −2.59431 1.00000 −1.49267 −2.59431 1.08103 1.00000 3.73042 −1.49267
1.14 1.00000 −2.44392 1.00000 2.01179 −2.44392 1.54759 1.00000 2.97273 2.01179
1.15 1.00000 −2.41544 1.00000 3.01333 −2.41544 −2.26454 1.00000 2.83435 3.01333
1.16 1.00000 −2.39250 1.00000 1.27700 −2.39250 3.72505 1.00000 2.72406 1.27700
1.17 1.00000 −2.32778 1.00000 2.23848 −2.32778 3.76217 1.00000 2.41856 2.23848
1.18 1.00000 −2.32502 1.00000 −1.28151 −2.32502 −2.20923 1.00000 2.40572 −1.28151
1.19 1.00000 −2.26664 1.00000 −3.59818 −2.26664 5.23582 1.00000 2.13767 −3.59818
1.20 1.00000 −2.21370 1.00000 0.840207 −2.21370 −5.05822 1.00000 1.90049 0.840207
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.96
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(4013\) \(1\)