Properties

Label 6035.2.a.g
Level 6035
Weight 2
Character orbit 6035.a
Self dual Yes
Analytic conductor 48.190
Analytic rank 0
Dimension 58
CM No

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Newspace parameters

Level: \( N \) = \( 6035 = 5 \cdot 17 \cdot 71 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1897176198\)
Analytic rank: \(0\)
Dimension: \(58\)
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.

\(\operatorname{Tr}(f)(q) = \) \(58q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut +\mathstrut 58q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 84q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(58q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut +\mathstrut 58q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 84q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 28q^{11} \) \(\mathstrut +\mathstrut 18q^{12} \) \(\mathstrut +\mathstrut 37q^{13} \) \(\mathstrut +\mathstrut 28q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut +\mathstrut 58q^{17} \) \(\mathstrut -\mathstrut 12q^{18} \) \(\mathstrut +\mathstrut 19q^{19} \) \(\mathstrut +\mathstrut 69q^{20} \) \(\mathstrut +\mathstrut 31q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 13q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut +\mathstrut 18q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 60q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 39q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut +\mathstrut 113q^{36} \) \(\mathstrut +\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 3q^{40} \) \(\mathstrut +\mathstrut 65q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut +\mathstrut 17q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 14q^{48} \) \(\mathstrut +\mathstrut 117q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 61q^{52} \) \(\mathstrut +\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 105q^{56} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 34q^{58} \) \(\mathstrut +\mathstrut 22q^{59} \) \(\mathstrut +\mathstrut 18q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut -\mathstrut 19q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 89q^{64} \) \(\mathstrut +\mathstrut 37q^{65} \) \(\mathstrut -\mathstrut 37q^{66} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 69q^{68} \) \(\mathstrut +\mathstrut 75q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 17q^{72} \) \(\mathstrut +\mathstrut 49q^{73} \) \(\mathstrut +\mathstrut 29q^{74} \) \(\mathstrut +\mathstrut 6q^{75} \) \(\mathstrut -\mathstrut 6q^{76} \) \(\mathstrut +\mathstrut 17q^{77} \) \(\mathstrut -\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 7q^{79} \) \(\mathstrut +\mathstrut 83q^{80} \) \(\mathstrut +\mathstrut 134q^{81} \) \(\mathstrut +\mathstrut 7q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 18q^{84} \) \(\mathstrut +\mathstrut 58q^{85} \) \(\mathstrut +\mathstrut 23q^{86} \) \(\mathstrut -\mathstrut 36q^{87} \) \(\mathstrut -\mathstrut 33q^{88} \) \(\mathstrut +\mathstrut 52q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 80q^{92} \) \(\mathstrut -\mathstrut 37q^{93} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut +\mathstrut 19q^{95} \) \(\mathstrut -\mathstrut 35q^{96} \) \(\mathstrut +\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 33q^{98} \) \(\mathstrut +\mathstrut 57q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.80026 1.99842 5.84147 1.00000 −5.59610 −4.62775 −10.7571 0.993679 −2.80026
1.2 −2.75680 2.57899 5.59996 1.00000 −7.10976 3.29093 −9.92438 3.65117 −2.75680
1.3 −2.70439 −2.73763 5.31370 1.00000 7.40360 −4.83847 −8.96152 4.49461 −2.70439
1.4 −2.68796 −2.40870 5.22515 1.00000 6.47449 1.33386 −8.66909 2.80181 −2.68796
1.5 −2.49259 −0.124755 4.21303 1.00000 0.310963 1.75866 −5.51618 −2.98444 −2.49259
1.6 −2.45480 −1.45794 4.02604 1.00000 3.57896 −2.38415 −4.97353 −0.874405 −2.45480
1.7 −2.40526 1.86065 3.78528 1.00000 −4.47536 2.19847 −4.29406 0.462037 −2.40526
1.8 −2.20983 3.43880 2.88333 1.00000 −7.59915 −1.16489 −1.95201 8.82536 −2.20983
1.9 −2.17363 0.623249 2.72466 1.00000 −1.35471 −4.14588 −1.57514 −2.61156 −2.17363
1.10 −2.15077 −3.16911 2.62583 1.00000 6.81604 −1.54855 −1.34601 7.04327 −2.15077
1.11 −2.12400 −1.09989 2.51137 1.00000 2.33617 5.15845 −1.08615 −1.79024 −2.12400
1.12 −2.00836 0.177134 2.03352 1.00000 −0.355749 −1.65376 −0.0673116 −2.96862 −2.00836
1.13 −1.83919 1.25269 1.38262 1.00000 −2.30393 1.52576 1.13547 −1.43078 −1.83919
1.14 −1.67839 3.22950 0.816985 1.00000 −5.42036 0.934275 1.98556 7.42970 −1.67839
1.15 −1.56061 −2.33055 0.435498 1.00000 3.63707 3.61265 2.44157 2.43146 −1.56061
1.16 −1.54425 −3.31836 0.384710 1.00000 5.12438 3.26635 2.49441 8.01151 −1.54425
1.17 −1.51455 1.68592 0.293855 1.00000 −2.55340 −0.258342 2.58404 −0.157685 −1.51455
1.18 −1.30337 −0.487797 −0.301228 1.00000 0.635780 −1.77737 2.99935 −2.76205 −1.30337
1.19 −1.22809 1.74628 −0.491793 1.00000 −2.14460 4.49008 3.06015 0.0495068 −1.22809
1.20 −1.22218 −2.16829 −0.506288 1.00000 2.65003 −1.52570 3.06312 1.70146 −1.22218
See all 58 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.58
Significant digits:
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Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(17\) \(-1\)
\(71\) \(-1\)