Properties

Label 8043.2.a.r
Level 8043
Weight 2
Character orbit 8043.a
Self dual Yes
Analytic conductor 64.224
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(1\)
Dimension: \(46\)
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.

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

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 −2.74370 −1.00000 5.52791 −1.87586 2.74370 −1.00000 −9.67954 1.00000 5.14679
1.2 −2.68548 −1.00000 5.21178 2.43353 2.68548 −1.00000 −8.62517 1.00000 −6.53519
1.3 −2.54493 −1.00000 4.47665 0.653154 2.54493 −1.00000 −6.30289 1.00000 −1.66223
1.4 −2.41337 −1.00000 3.82437 1.40118 2.41337 −1.00000 −4.40289 1.00000 −3.38157
1.5 −2.37441 −1.00000 3.63784 −1.15289 2.37441 −1.00000 −3.88892 1.00000 2.73743
1.6 −2.17399 −1.00000 2.72624 −2.42046 2.17399 −1.00000 −1.57885 1.00000 5.26206
1.7 −2.13482 −1.00000 2.55746 −3.00499 2.13482 −1.00000 −1.19007 1.00000 6.41512
1.8 −1.90871 −1.00000 1.64317 2.98743 1.90871 −1.00000 0.681087 1.00000 −5.70214
1.9 −1.80468 −1.00000 1.25687 −3.36288 1.80468 −1.00000 1.34111 1.00000 6.06893
1.10 −1.77170 −1.00000 1.13894 3.36587 1.77170 −1.00000 1.52555 1.00000 −5.96332
1.11 −1.68230 −1.00000 0.830121 −0.636152 1.68230 −1.00000 1.96808 1.00000 1.07020
1.12 −1.59029 −1.00000 0.529036 3.24933 1.59029 −1.00000 2.33927 1.00000 −5.16740
1.13 −1.51659 −1.00000 0.300048 −2.76194 1.51659 −1.00000 2.57813 1.00000 4.18873
1.14 −1.34694 −1.00000 −0.185749 −2.41165 1.34694 −1.00000 2.94408 1.00000 3.24834
1.15 −0.944841 −1.00000 −1.10728 3.73621 0.944841 −1.00000 2.93588 1.00000 −3.53012
1.16 −0.861946 −1.00000 −1.25705 1.66275 0.861946 −1.00000 2.80740 1.00000 −1.43320
1.17 −0.696464 −1.00000 −1.51494 1.11267 0.696464 −1.00000 2.44803 1.00000 −0.774934
1.18 −0.661222 −1.00000 −1.56279 −1.64966 0.661222 −1.00000 2.35579 1.00000 1.09079
1.19 −0.522616 −1.00000 −1.72687 −3.91798 0.522616 −1.00000 1.94772 1.00000 2.04760
1.20 −0.490976 −1.00000 −1.75894 0.513476 0.490976 −1.00000 1.84555 1.00000 −0.252105
See all 46 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.46
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(7\) \(1\)
\(383\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8043))\):

\(T_{2}^{46} - \cdots\)
\(T_{5}^{46} + \cdots\)
\(T_{11}^{46} - \cdots\)