Properties

Label 10.14.a.b
Level 10
Weight 14
Character orbit 10.a
Self dual yes
Analytic conductor 10.723
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 14 \)
Character orbit: \([\chi]\) = 10.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.7230928952\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 64q^{2} + 1224q^{3} + 4096q^{4} + 15625q^{5} - 78336q^{6} - 65212q^{7} - 262144q^{8} - 96147q^{9} + O(q^{10}) \) \( q - 64q^{2} + 1224q^{3} + 4096q^{4} + 15625q^{5} - 78336q^{6} - 65212q^{7} - 262144q^{8} - 96147q^{9} - 1000000q^{10} + 7427652q^{11} + 5013504q^{12} + 32243054q^{13} + 4173568q^{14} + 19125000q^{15} + 16777216q^{16} - 20088222q^{17} + 6153408q^{18} + 77070740q^{19} + 64000000q^{20} - 79819488q^{21} - 475369728q^{22} + 664071804q^{23} - 320864256q^{24} + 244140625q^{25} - 2063555456q^{26} - 2069135280q^{27} - 267108352q^{28} + 1558250670q^{29} - 1224000000q^{30} - 303290968q^{31} - 1073741824q^{32} + 9091446048q^{33} + 1285646208q^{34} - 1018937500q^{35} - 393818112q^{36} - 775029322q^{37} - 4932527360q^{38} + 39465498096q^{39} - 4096000000q^{40} + 43696205082q^{41} + 5108447232q^{42} - 68680553536q^{43} + 30423662592q^{44} - 1502296875q^{45} - 42500595456q^{46} - 138979393812q^{47} + 20535312384q^{48} - 92636405463q^{49} - 15625000000q^{50} - 24587983728q^{51} + 132067549184q^{52} - 103656826986q^{53} + 132424657920q^{54} + 116057062500q^{55} + 17094934528q^{56} + 94334585760q^{57} - 99728042880q^{58} + 394887188940q^{59} + 78336000000q^{60} - 488570895538q^{61} + 19410621952q^{62} + 6269938164q^{63} + 68719476736q^{64} + 503797718750q^{65} - 581852547072q^{66} + 368381730848q^{67} - 82281357312q^{68} + 812823888096q^{69} + 65212000000q^{70} + 325473704592q^{71} + 25204359168q^{72} - 2262556998406q^{73} + 49601876608q^{74} + 298828125000q^{75} + 315681751040q^{76} - 484372042224q^{77} - 2525791878144q^{78} + 2032917332000q^{79} + 262144000000q^{80} - 2379332209239q^{81} - 2796557125248q^{82} - 854518199496q^{83} - 326940622848q^{84} - 313878468750q^{85} + 4395555426304q^{86} + 1907298820080q^{87} - 1947114405888q^{88} + 8906829484890q^{89} + 96147000000q^{90} - 2102634037448q^{91} + 2720038109184q^{92} - 371228144832q^{93} + 8894681203968q^{94} + 1204230312500q^{95} - 1314259992576q^{96} - 9873550533742q^{97} + 5928729949632q^{98} - 714146456844q^{99} + O(q^{100}) \)

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
−64.0000 1224.00 4096.00 15625.0 −78336.0 −65212.0 −262144. −96147.0 −1.00000e6
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 10.14.a.b 1
3.b odd 2 1 90.14.a.e 1
4.b odd 2 1 80.14.a.a 1
5.b even 2 1 50.14.a.c 1
5.c odd 4 2 50.14.b.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
10.14.a.b 1 1.a even 1 1 trivial
50.14.a.c 1 5.b even 2 1
50.14.b.b 2 5.c odd 4 2
80.14.a.a 1 4.b odd 2 1
90.14.a.e 1 3.b odd 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 1224 \) acting on \(S_{14}^{\mathrm{new}}(\Gamma_0(10))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 64 T \)
$3$ \( 1 - 1224 T + 1594323 T^{2} \)
$5$ \( 1 - 15625 T \)
$7$ \( 1 + 65212 T + 96889010407 T^{2} \)
$11$ \( 1 - 7427652 T + 34522712143931 T^{2} \)
$13$ \( 1 - 32243054 T + 302875106592253 T^{2} \)
$17$ \( 1 + 20088222 T + 9904578032905937 T^{2} \)
$19$ \( 1 - 77070740 T + 42052983462257059 T^{2} \)
$23$ \( 1 - 664071804 T + 504036361936467383 T^{2} \)
$29$ \( 1 - 1558250670 T + 10260628712958602189 T^{2} \)
$31$ \( 1 + 303290968 T + 24417546297445042591 T^{2} \)
$37$ \( 1 + 775029322 T + \)\(24\!\cdots\!97\)\( T^{2} \)
$41$ \( 1 - 43696205082 T + \)\(92\!\cdots\!21\)\( T^{2} \)
$43$ \( 1 + 68680553536 T + \)\(17\!\cdots\!43\)\( T^{2} \)
$47$ \( 1 + 138979393812 T + \)\(54\!\cdots\!27\)\( T^{2} \)
$53$ \( 1 + 103656826986 T + \)\(26\!\cdots\!73\)\( T^{2} \)
$59$ \( 1 - 394887188940 T + \)\(10\!\cdots\!79\)\( T^{2} \)
$61$ \( 1 + 488570895538 T + \)\(16\!\cdots\!81\)\( T^{2} \)
$67$ \( 1 - 368381730848 T + \)\(54\!\cdots\!87\)\( T^{2} \)
$71$ \( 1 - 325473704592 T + \)\(11\!\cdots\!11\)\( T^{2} \)
$73$ \( 1 + 2262556998406 T + \)\(16\!\cdots\!33\)\( T^{2} \)
$79$ \( 1 - 2032917332000 T + \)\(46\!\cdots\!39\)\( T^{2} \)
$83$ \( 1 + 854518199496 T + \)\(88\!\cdots\!63\)\( T^{2} \)
$89$ \( 1 - 8906829484890 T + \)\(21\!\cdots\!69\)\( T^{2} \)
$97$ \( 1 + 9873550533742 T + \)\(67\!\cdots\!77\)\( T^{2} \)
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