Properties

Label 6.26.a.c
Level $6$
Weight $26$
Character orbit 6.a
Self dual yes
Analytic conductor $23.760$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 6.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.7598067971\)
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

\(f(q)\) \(=\) \( q + 4096 q^{2} - 531441 q^{3} + 16777216 q^{4} - 799327650 q^{5} - 2176782336 q^{6} + 7962409664 q^{7} + 68719476736 q^{8} + 282429536481 q^{9} + O(q^{10}) \) \( q + 4096 q^{2} - 531441 q^{3} + 16777216 q^{4} - 799327650 q^{5} - 2176782336 q^{6} + 7962409664 q^{7} + 68719476736 q^{8} + 282429536481 q^{9} - 3274046054400 q^{10} - 1760169438780 q^{11} - 8916100448256 q^{12} + 164197771122398 q^{13} + 32614029983744 q^{14} + 424795485643650 q^{15} + 281474976710656 q^{16} - 2377485783158526 q^{17} + 1156831381426176 q^{18} + 10628455411412156 q^{19} - 13410492638822400 q^{20} - 4231550954245824 q^{21} - 7209654021242880 q^{22} + 76636270038478200 q^{23} - 36520347436056576 q^{24} + 340901468177569375 q^{25} + 672554070517342208 q^{26} - 150094635296999121 q^{27} + 133587066813415424 q^{28} + 2409286328905759014 q^{29} + 1739962309196390400 q^{30} + 5300292736548162248 q^{31} + 1152921504606846976 q^{32} + 935426206714681980 q^{33} - 9738181767817322496 q^{34} - 6364574205062409600 q^{35} + 4738381338321616896 q^{36} + 8422279761396447398 q^{37} + 43534153365144190976 q^{38} - 87261427683058315518 q^{39} - 54929377848616550400 q^{40} + 96949933961364240954 q^{41} - 17332432708590895104 q^{42} - 366142029096077360956 q^{43} - 29530742871010836480 q^{44} - 225753737685946999650 q^{45} + 313902162077606707200 q^{46} - 1096120516310397836160 q^{47} - 149587343098087735296 q^{48} - 1277668652006604307911 q^{49} + 1396332413655324160000 q^{50} + 1263493422087550215966 q^{51} + 2754781472839033683968 q^{52} + 6643878547982153683806 q^{53} - 614787626176508399616 q^{54} + 1406952101101836267000 q^{55} + 547172625667749576704 q^{56} - 5648396972296287596796 q^{57} + 9868436803197988921344 q^{58} - 18570975137188311995580 q^{59} + 7126885618468415078400 q^{60} + 181090625412505219550 q^{61} + 21709999048901272567808 q^{62} + 2248819670675354952384 q^{63} + 4722366482869645213696 q^{64} - 131247818526504255704700 q^{65} + 3831505742703337390080 q^{66} + 42722727941919151153724 q^{67} - 39887592520979752943616 q^{68} - 40727655985518893086200 q^{69} - 26069295943935629721600 q^{70} + 97511777003879914759560 q^{71} + 19408409961765342806016 q^{72} + 21327862984057460410058 q^{73} + 34497657902679848542208 q^{74} - 181169017149755646219375 q^{75} + 178315892183630606237696 q^{76} - 14015190149619328369920 q^{77} - 357422807789806860361728 q^{78} + 851442782353667806307768 q^{79} - 224990731667933390438400 q^{80} + 79766443076872509863361 q^{81} + 397106929505747930947584 q^{82} + 775507317775664307451068 q^{83} - 70993644374388306345984 q^{84} + 1900390123960514165043900 q^{85} - 1499717751177532870475776 q^{86} - 1280393535920005476159174 q^{87} - 120957922799660386222080 q^{88} - 140037916661933135837382 q^{89} - 924687309561638910566400 q^{90} + 1307409919592241962054272 q^{91} + 1285743255869877072691200 q^{92} - 2816792872203891893239368 q^{93} - 4489709634807389536911360 q^{94} - 8495618287133861836913400 q^{95} - 612709757329767363772416 q^{96} + 5087878316240127424118018 q^{97} - 5233330798619051245203456 q^{98} - 497123838722657306133180 q^{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
4096.00 −531441. 1.67772e7 −7.99328e8 −2.17678e9 7.96241e9 6.87195e10 2.82430e11 −3.27405e12
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)

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 6.26.a.c 1
3.b odd 2 1 18.26.a.a 1
4.b odd 2 1 48.26.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6.26.a.c 1 1.a even 1 1 trivial
18.26.a.a 1 3.b odd 2 1
48.26.a.b 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} + 799327650 \) acting on \(S_{26}^{\mathrm{new}}(\Gamma_0(6))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -4096 + T \)
$3$ \( 531441 + T \)
$5$ \( 799327650 + T \)
$7$ \( -7962409664 + T \)
$11$ \( 1760169438780 + T \)
$13$ \( -164197771122398 + T \)
$17$ \( 2377485783158526 + T \)
$19$ \( -10628455411412156 + T \)
$23$ \( -76636270038478200 + T \)
$29$ \( -2409286328905759014 + T \)
$31$ \( -5300292736548162248 + T \)
$37$ \( -8422279761396447398 + T \)
$41$ \( -96949933961364240954 + T \)
$43$ \( \)\(36\!\cdots\!56\)\( + T \)
$47$ \( \)\(10\!\cdots\!60\)\( + T \)
$53$ \( -\)\(66\!\cdots\!06\)\( + T \)
$59$ \( \)\(18\!\cdots\!80\)\( + T \)
$61$ \( -\)\(18\!\cdots\!50\)\( + T \)
$67$ \( -\)\(42\!\cdots\!24\)\( + T \)
$71$ \( -\)\(97\!\cdots\!60\)\( + T \)
$73$ \( -\)\(21\!\cdots\!58\)\( + T \)
$79$ \( -\)\(85\!\cdots\!68\)\( + T \)
$83$ \( -\)\(77\!\cdots\!68\)\( + T \)
$89$ \( \)\(14\!\cdots\!82\)\( + T \)
$97$ \( -\)\(50\!\cdots\!18\)\( + T \)
show more
show less