Properties

Label 6035.2.a.h
Level 6035
Weight 2
Character orbit 6035.a
Self dual Yes
Analytic conductor 48.190
Analytic rank 0
Dimension 59
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: \(59\)
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.

\(\operatorname{Tr}(f)(q) = \) \(59q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 76q^{4} \) \(\mathstrut +\mathstrut 59q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(59q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 76q^{4} \) \(\mathstrut +\mathstrut 59q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 16q^{12} \) \(\mathstrut +\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 114q^{16} \) \(\mathstrut -\mathstrut 59q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 35q^{19} \) \(\mathstrut +\mathstrut 76q^{20} \) \(\mathstrut +\mathstrut 41q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 35q^{24} \) \(\mathstrut +\mathstrut 59q^{25} \) \(\mathstrut +\mathstrut 10q^{26} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut +\mathstrut 28q^{28} \) \(\mathstrut +\mathstrut 10q^{29} \) \(\mathstrut +\mathstrut 14q^{30} \) \(\mathstrut +\mathstrut 15q^{31} \) \(\mathstrut +\mathstrut 19q^{32} \) \(\mathstrut -\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut +\mathstrut 9q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut +\mathstrut 17q^{38} \) \(\mathstrut +\mathstrut 25q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 47q^{41} \) \(\mathstrut +\mathstrut 46q^{42} \) \(\mathstrut +\mathstrut 27q^{43} \) \(\mathstrut +\mathstrut 39q^{44} \) \(\mathstrut +\mathstrut 97q^{45} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 58q^{48} \) \(\mathstrut +\mathstrut 174q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 13q^{52} \) \(\mathstrut +\mathstrut 17q^{53} \) \(\mathstrut +\mathstrut 48q^{54} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut +\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 6q^{57} \) \(\mathstrut +\mathstrut 32q^{58} \) \(\mathstrut +\mathstrut 30q^{59} \) \(\mathstrut +\mathstrut 16q^{60} \) \(\mathstrut +\mathstrut 85q^{61} \) \(\mathstrut -\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 14q^{63} \) \(\mathstrut +\mathstrut 168q^{64} \) \(\mathstrut +\mathstrut 25q^{65} \) \(\mathstrut +\mathstrut 87q^{66} \) \(\mathstrut +\mathstrut 21q^{67} \) \(\mathstrut -\mathstrut 76q^{68} \) \(\mathstrut +\mathstrut 111q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 52q^{72} \) \(\mathstrut +\mathstrut 41q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut +\mathstrut 6q^{75} \) \(\mathstrut +\mathstrut 118q^{76} \) \(\mathstrut +\mathstrut 55q^{77} \) \(\mathstrut -\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 43q^{79} \) \(\mathstrut +\mathstrut 114q^{80} \) \(\mathstrut +\mathstrut 207q^{81} \) \(\mathstrut +\mathstrut 45q^{82} \) \(\mathstrut +\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 62q^{84} \) \(\mathstrut -\mathstrut 59q^{85} \) \(\mathstrut +\mathstrut 19q^{86} \) \(\mathstrut +\mathstrut 8q^{87} \) \(\mathstrut +\mathstrut 35q^{88} \) \(\mathstrut +\mathstrut 86q^{89} \) \(\mathstrut +\mathstrut 3q^{90} \) \(\mathstrut +\mathstrut 47q^{91} \) \(\mathstrut -\mathstrut 98q^{92} \) \(\mathstrut +\mathstrut 41q^{93} \) \(\mathstrut +\mathstrut 30q^{94} \) \(\mathstrut +\mathstrut 35q^{95} \) \(\mathstrut +\mathstrut 69q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 14q^{98} \) \(\mathstrut +\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.78220 0.531208 5.74064 1.00000 −1.47793 5.08298 −10.4072 −2.71782 −2.78220
1.2 −2.75521 −3.32287 5.59117 1.00000 9.15519 0.0853844 −9.89442 8.04146 −2.75521
1.3 −2.69345 3.39811 5.25470 1.00000 −9.15266 −4.44179 −8.76637 8.54717 −2.69345
1.4 −2.65295 −2.09005 5.03815 1.00000 5.54480 2.26446 −8.06007 1.36830 −2.65295
1.5 −2.48619 −1.43684 4.18113 1.00000 3.57226 −2.10057 −5.42270 −0.935481 −2.48619
1.6 −2.46188 1.88140 4.06087 1.00000 −4.63179 −1.20679 −5.07361 0.539668 −2.46188
1.7 −2.44774 0.819540 3.99145 1.00000 −2.00602 2.11487 −4.87457 −2.32835 −2.44774
1.8 −2.42937 −1.27159 3.90183 1.00000 3.08915 −3.98798 −4.62024 −1.38307 −2.42937
1.9 −2.25292 1.80225 3.07566 1.00000 −4.06033 −3.69213 −2.42337 0.248105 −2.25292
1.10 −2.17980 2.67247 2.75152 1.00000 −5.82545 4.07077 −1.63817 4.14211 −2.17980
1.11 −2.11526 3.31197 2.47433 1.00000 −7.00568 4.53334 −1.00333 7.96913 −2.11526
1.12 −2.03514 −3.16809 2.14178 1.00000 6.44749 −3.29825 −0.288547 7.03677 −2.03514
1.13 −1.96419 −0.830203 1.85806 1.00000 1.63068 −0.855688 0.278801 −2.31076 −1.96419
1.14 −1.75849 −0.492394 1.09228 1.00000 0.865869 1.61123 1.59622 −2.75755 −1.75849
1.15 −1.71705 −3.23330 0.948270 1.00000 5.55174 4.30663 1.80588 7.45420 −1.71705
1.16 −1.47530 −1.44851 0.176504 1.00000 2.13699 2.79346 2.69020 −0.901812 −1.47530
1.17 −1.34008 −2.63171 −0.204177 1.00000 3.52671 −4.96340 2.95378 3.92590 −1.34008
1.18 −1.27257 0.337599 −0.380563 1.00000 −0.429619 −3.22826 3.02944 −2.88603 −1.27257
1.19 −1.25970 2.36319 −0.413145 1.00000 −2.97691 2.52906 3.03985 2.58464 −1.25970
1.20 −1.15770 0.151800 −0.659734 1.00000 −0.175739 −1.47605 3.07917 −2.97696 −1.15770
See all 59 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.59
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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