Properties

Label 10.6.a.a
Level 10
Weight 6
Character orbit 10.a
Self dual Yes
Analytic conductor 1.604
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 10.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.60383819813\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 4q^{2} - 26q^{3} + 16q^{4} - 25q^{5} + 104q^{6} - 22q^{7} - 64q^{8} + 433q^{9} + O(q^{10}) \) \( q - 4q^{2} - 26q^{3} + 16q^{4} - 25q^{5} + 104q^{6} - 22q^{7} - 64q^{8} + 433q^{9} + 100q^{10} - 768q^{11} - 416q^{12} - 46q^{13} + 88q^{14} + 650q^{15} + 256q^{16} + 378q^{17} - 1732q^{18} + 1100q^{19} - 400q^{20} + 572q^{21} + 3072q^{22} - 1986q^{23} + 1664q^{24} + 625q^{25} + 184q^{26} - 4940q^{27} - 352q^{28} - 5610q^{29} - 2600q^{30} - 3988q^{31} - 1024q^{32} + 19968q^{33} - 1512q^{34} + 550q^{35} + 6928q^{36} - 142q^{37} - 4400q^{38} + 1196q^{39} + 1600q^{40} + 1542q^{41} - 2288q^{42} - 5026q^{43} - 12288q^{44} - 10825q^{45} + 7944q^{46} + 24738q^{47} - 6656q^{48} - 16323q^{49} - 2500q^{50} - 9828q^{51} - 736q^{52} - 14166q^{53} + 19760q^{54} + 19200q^{55} + 1408q^{56} - 28600q^{57} + 22440q^{58} + 28380q^{59} + 10400q^{60} + 5522q^{61} + 15952q^{62} - 9526q^{63} + 4096q^{64} + 1150q^{65} - 79872q^{66} - 24742q^{67} + 6048q^{68} + 51636q^{69} - 2200q^{70} + 42372q^{71} - 27712q^{72} - 52126q^{73} + 568q^{74} - 16250q^{75} + 17600q^{76} + 16896q^{77} - 4784q^{78} - 39640q^{79} - 6400q^{80} + 23221q^{81} - 6168q^{82} - 59826q^{83} + 9152q^{84} - 9450q^{85} + 20104q^{86} + 145860q^{87} + 49152q^{88} + 57690q^{89} + 43300q^{90} + 1012q^{91} - 31776q^{92} + 103688q^{93} - 98952q^{94} - 27500q^{95} + 26624q^{96} - 144382q^{97} + 65292q^{98} - 332544q^{99} + O(q^{100}) \)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
−4.00000 −26.0000 16.0000 −25.0000 104.000 −22.0000 −64.0000 433.000 100.000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{3} + 26 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(10))\).