Properties

Label 10.14.a.c
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

\(f(q)\) \(=\) \( q + 64q^{2} - 2394q^{3} + 4096q^{4} - 15625q^{5} - 153216q^{6} + 438122q^{7} + 262144q^{8} + 4136913q^{9} + O(q^{10}) \) \( q + 64q^{2} - 2394q^{3} + 4096q^{4} - 15625q^{5} - 153216q^{6} + 438122q^{7} + 262144q^{8} + 4136913q^{9} - 1000000q^{10} - 1608288q^{11} - 9805824q^{12} + 2653106q^{13} + 28039808q^{14} + 37406250q^{15} + 16777216q^{16} + 108907962q^{17} + 264762432q^{18} - 63937300q^{19} - 64000000q^{20} - 1048864068q^{21} - 102930432q^{22} + 1123819326q^{23} - 627572736q^{24} + 244140625q^{25} + 169798784q^{26} - 6086960460q^{27} + 1794547712q^{28} + 2080484790q^{29} + 2394000000q^{30} - 6556003348q^{31} + 1073741824q^{32} + 3850241472q^{33} + 6970109568q^{34} - 6845656250q^{35} + 16944795648q^{36} + 18286017362q^{37} - 4091987200q^{38} - 6351535764q^{39} - 4096000000q^{40} + 39390632262q^{41} - 67127300352q^{42} - 11907272674q^{43} - 6587547648q^{44} - 64639265625q^{45} + 71924436864q^{46} + 66374501922q^{47} - 40164655104q^{48} + 95061876477q^{49} + 15625000000q^{50} - 260725661028q^{51} + 10867122176q^{52} + 36595449546q^{53} - 389565469440q^{54} + 25129500000q^{55} + 114851053568q^{56} + 153065896200q^{57} + 133151026560q^{58} - 318466174020q^{59} + 153216000000q^{60} + 343346468402q^{61} - 419584214272q^{62} + 1812472597386q^{63} + 68719476736q^{64} - 41454781250q^{65} + 246415454208q^{66} + 564706251482q^{67} + 446087012352q^{68} - 2690423466444q^{69} - 438122000000q^{70} - 1454128449468q^{71} + 1084466921472q^{72} - 1708261304734q^{73} + 1170305111168q^{74} - 584472656250q^{75} - 261887180800q^{76} - 704626355136q^{77} - 406498288896q^{78} - 1923992449240q^{79} - 262144000000q^{80} + 7976607796341q^{81} + 2521000464768q^{82} + 175733708046q^{83} - 4296147222528q^{84} - 1701686906250q^{85} - 762065451136q^{86} - 4980680587260q^{87} - 421603049472q^{88} + 3079262817690q^{89} - 4136913000000q^{90} + 1162384106932q^{91} + 4603163959296q^{92} + 15695072015112q^{93} + 4247968123008q^{94} + 999020312500q^{95} - 2570537926656q^{96} - 3952362173758q^{97} + 6083960094528q^{98} - 6653347534944q^{99} + O(q^{100}) \)

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 −2394.00 4096.00 −15625.0 −153216. 438122. 262144. 4.13691e6 −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.c 1
3.b odd 2 1 90.14.a.d 1
4.b odd 2 1 80.14.a.c 1
5.b even 2 1 50.14.a.b 1
5.c odd 4 2 50.14.b.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
10.14.a.c 1 1.a even 1 1 trivial
50.14.a.b 1 5.b even 2 1
50.14.b.a 2 5.c odd 4 2
80.14.a.c 1 4.b odd 2 1
90.14.a.d 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 \( T_{3} + 2394 \) acting on \(S_{14}^{\mathrm{new}}(\Gamma_0(10))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - 64 T \)
$3$ \( 1 + 2394 T + 1594323 T^{2} \)
$5$ \( 1 + 15625 T \)
$7$ \( 1 - 438122 T + 96889010407 T^{2} \)
$11$ \( 1 + 1608288 T + 34522712143931 T^{2} \)
$13$ \( 1 - 2653106 T + 302875106592253 T^{2} \)
$17$ \( 1 - 108907962 T + 9904578032905937 T^{2} \)
$19$ \( 1 + 63937300 T + 42052983462257059 T^{2} \)
$23$ \( 1 - 1123819326 T + 504036361936467383 T^{2} \)
$29$ \( 1 - 2080484790 T + 10260628712958602189 T^{2} \)
$31$ \( 1 + 6556003348 T + 24417546297445042591 T^{2} \)
$37$ \( 1 - 18286017362 T + \)\(24\!\cdots\!97\)\( T^{2} \)
$41$ \( 1 - 39390632262 T + \)\(92\!\cdots\!21\)\( T^{2} \)
$43$ \( 1 + 11907272674 T + \)\(17\!\cdots\!43\)\( T^{2} \)
$47$ \( 1 - 66374501922 T + \)\(54\!\cdots\!27\)\( T^{2} \)
$53$ \( 1 - 36595449546 T + \)\(26\!\cdots\!73\)\( T^{2} \)
$59$ \( 1 + 318466174020 T + \)\(10\!\cdots\!79\)\( T^{2} \)
$61$ \( 1 - 343346468402 T + \)\(16\!\cdots\!81\)\( T^{2} \)
$67$ \( 1 - 564706251482 T + \)\(54\!\cdots\!87\)\( T^{2} \)
$71$ \( 1 + 1454128449468 T + \)\(11\!\cdots\!11\)\( T^{2} \)
$73$ \( 1 + 1708261304734 T + \)\(16\!\cdots\!33\)\( T^{2} \)
$79$ \( 1 + 1923992449240 T + \)\(46\!\cdots\!39\)\( T^{2} \)
$83$ \( 1 - 175733708046 T + \)\(88\!\cdots\!63\)\( T^{2} \)
$89$ \( 1 - 3079262817690 T + \)\(21\!\cdots\!69\)\( T^{2} \)
$97$ \( 1 + 3952362173758 T + \)\(67\!\cdots\!77\)\( T^{2} \)
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