Properties

Label 6034.2.a.o
Level 6034
Weight 2
Character orbit 6034.a
Self dual Yes
Analytic conductor 48.182
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(1\)
Dimension: \(25\)
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.

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

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 −3.32592 1.00000 4.15520 3.32592 −1.00000 −1.00000 8.06177 −4.15520
1.2 −1.00000 −3.01499 1.00000 0.160841 3.01499 −1.00000 −1.00000 6.09019 −0.160841
1.3 −1.00000 −2.93664 1.00000 1.14962 2.93664 −1.00000 −1.00000 5.62386 −1.14962
1.4 −1.00000 −2.89955 1.00000 −3.35107 2.89955 −1.00000 −1.00000 5.40739 3.35107
1.5 −1.00000 −2.44573 1.00000 1.36313 2.44573 −1.00000 −1.00000 2.98159 −1.36313
1.6 −1.00000 −2.25211 1.00000 2.47943 2.25211 −1.00000 −1.00000 2.07199 −2.47943
1.7 −1.00000 −1.45476 1.00000 0.421306 1.45476 −1.00000 −1.00000 −0.883670 −0.421306
1.8 −1.00000 −1.28274 1.00000 −1.76478 1.28274 −1.00000 −1.00000 −1.35459 1.76478
1.9 −1.00000 −1.09451 1.00000 −2.81071 1.09451 −1.00000 −1.00000 −1.80204 2.81071
1.10 −1.00000 −0.804173 1.00000 −3.18296 0.804173 −1.00000 −1.00000 −2.35331 3.18296
1.11 −1.00000 −0.655704 1.00000 −2.51498 0.655704 −1.00000 −1.00000 −2.57005 2.51498
1.12 −1.00000 −0.642803 1.00000 −0.120045 0.642803 −1.00000 −1.00000 −2.58680 0.120045
1.13 −1.00000 −0.286451 1.00000 3.05880 0.286451 −1.00000 −1.00000 −2.91795 −3.05880
1.14 −1.00000 −0.221832 1.00000 −0.411075 0.221832 −1.00000 −1.00000 −2.95079 0.411075
1.15 −1.00000 0.0257691 1.00000 3.06772 −0.0257691 −1.00000 −1.00000 −2.99934 −3.06772
1.16 −1.00000 0.684006 1.00000 2.60861 −0.684006 −1.00000 −1.00000 −2.53214 −2.60861
1.17 −1.00000 0.809571 1.00000 3.41286 −0.809571 −1.00000 −1.00000 −2.34460 −3.41286
1.18 −1.00000 0.817521 1.00000 −4.27702 −0.817521 −1.00000 −1.00000 −2.33166 4.27702
1.19 −1.00000 1.42126 1.00000 −0.924054 −1.42126 −1.00000 −1.00000 −0.980018 0.924054
1.20 −1.00000 1.89436 1.00000 0.229039 −1.89436 −1.00000 −1.00000 0.588591 −0.229039
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(1\)
\(431\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\):

\(T_{3}^{25} + \cdots\)
\(T_{5}^{25} - \cdots\)
\(T_{11}^{25} + \cdots\)