Properties

Label 6035.2.a.b
Level 6035
Weight 2
Character orbit 6035.a
Self dual Yes
Analytic conductor 48.190
Analytic rank 1
Dimension 36
CM No

Related objects

Downloads

Learn more about

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: \(1\)
Dimension: \(36\)
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.

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

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 −2.66525 0.180914 5.10356 1.00000 −0.482180 −2.30037 −8.27176 −2.96727 −2.66525
1.2 −2.40320 1.20051 3.77538 1.00000 −2.88508 −1.77185 −4.26659 −1.55876 −2.40320
1.3 −2.39029 −2.40790 3.71350 1.00000 5.75558 4.16969 −4.09576 2.79797 −2.39029
1.4 −2.31945 −2.05009 3.37984 1.00000 4.75509 0.529758 −3.20047 1.20289 −2.31945
1.5 −2.29064 1.47549 3.24701 1.00000 −3.37981 2.13493 −2.85645 −0.822934 −2.29064
1.6 −1.85242 0.130041 1.43148 1.00000 −0.240891 2.44217 1.05315 −2.98309 −1.85242
1.7 −1.71589 −3.02116 0.944266 1.00000 5.18397 −0.410823 1.81152 6.12740 −1.71589
1.8 −1.63901 0.960813 0.686340 1.00000 −1.57478 4.58027 2.15310 −2.07684 −1.63901
1.9 −1.62869 2.31397 0.652617 1.00000 −3.76873 −4.05639 2.19446 2.35446 −1.62869
1.10 −1.59880 −0.663250 0.556157 1.00000 1.06040 −3.10735 2.30841 −2.56010 −1.59880
1.11 −1.59058 2.74131 0.529934 1.00000 −4.36027 0.195561 2.33825 4.51480 −1.59058
1.12 −1.02277 −0.691517 −0.953933 1.00000 0.707265 1.61582 3.02121 −2.52180 −1.02277
1.13 −0.861525 −2.77636 −1.25777 1.00000 2.39191 0.623554 2.80665 4.70820 −0.861525
1.14 −0.644629 1.56810 −1.58445 1.00000 −1.01085 2.57685 2.31064 −0.541047 −0.644629
1.15 −0.619688 −2.94210 −1.61599 1.00000 1.82319 −1.69113 2.24078 5.65598 −0.619688
1.16 −0.381657 −0.970824 −1.85434 1.00000 0.370521 −3.53323 1.47103 −2.05750 −0.381657
1.17 −0.163606 −0.433822 −1.97323 1.00000 0.0709760 2.35725 0.650046 −2.81180 −0.163606
1.18 −0.134450 −0.934655 −1.98192 1.00000 0.125664 −1.20552 0.535370 −2.12642 −0.134450
1.19 −0.0473223 3.03750 −1.99776 1.00000 −0.143741 −2.32686 0.189183 6.22638 −0.0473223
1.20 0.111835 1.47233 −1.98749 1.00000 0.164659 −0.779752 −0.445943 −0.832238 0.111835
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.36
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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