Properties

Label 35.19.c.a
Level $35$
Weight $19$
Character orbit 35.c
Self dual yes
Analytic conductor $71.885$
Analytic rank $0$
Dimension $1$
CM discriminant -35
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 19 \)
Character orbit: \([\chi]\) \(=\) 35.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(71.8851481984\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \( q - 39286q^{3} + 262144q^{4} + 1953125q^{5} - 40353607q^{7} + 1155969307q^{9} + O(q^{10}) \) \( q - 39286q^{3} + 262144q^{4} + 1953125q^{5} - 40353607q^{7} + 1155969307q^{9} + 2637510122q^{11} - 10298589184q^{12} + 18822563674q^{13} - 76730468750q^{15} + 68719476736q^{16} - 54170520014q^{17} + 512000000000q^{20} + 1585331804602q^{21} + 3814697265625q^{25} - 30193208863948q^{27} - 10578455953408q^{28} - 14623240000822q^{29} - 103617222652892q^{33} - 78815638671875q^{35} + 303030418014208q^{36} - 739463236496764q^{39} + 691407453421568q^{44} + 2257752552734375q^{45} + 261032556546466q^{47} - 2699713363050496q^{48} + 1628413597910449q^{49} + 2128143049270004q^{51} + 4934222131757056q^{52} + 5151386957031250q^{55} - 20114432000000000q^{60} - 46647531118740349q^{63} + 18014398509481984q^{64} + 36762819675781250q^{65} - 14200476798550016q^{68} + 11592841444168322q^{71} + 100714945072821154q^{73} - 149864196777343750q^{75} - 106433046921710054q^{77} - 126856003456085902q^{79} + 134217728000000000q^{80} + 738324209242130005q^{81} + 367224638997840874q^{83} + 415585220585586688q^{84} - 105801796902343750q^{85} + 574488606672293092q^{87} - 759558337233072118q^{91} - 1519865703804919214q^{97} + 3048880747933825454q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
34.1
0
0 −39286.0 262144. 1.95312e6 0 −4.03536e7 0 1.15597e9 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
35.c odd 2 1 CM by \(\Q(\sqrt{-35}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 35.19.c.a 1
5.b even 2 1 35.19.c.b yes 1
7.b odd 2 1 35.19.c.b yes 1
35.c odd 2 1 CM 35.19.c.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.19.c.a 1 1.a even 1 1 trivial
35.19.c.a 1 35.c odd 2 1 CM
35.19.c.b yes 1 5.b even 2 1
35.19.c.b yes 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{19}^{\mathrm{new}}(35, [\chi])\):

\( T_{2} \)
\( T_{3} + 39286 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 39286 + T \)
$5$ \( -1953125 + T \)
$7$ \( 40353607 + T \)
$11$ \( -2637510122 + T \)
$13$ \( -18822563674 + T \)
$17$ \( 54170520014 + T \)
$19$ \( T \)
$23$ \( T \)
$29$ \( 14623240000822 + T \)
$31$ \( T \)
$37$ \( T \)
$41$ \( T \)
$43$ \( T \)
$47$ \( -261032556546466 + T \)
$53$ \( T \)
$59$ \( T \)
$61$ \( T \)
$67$ \( T \)
$71$ \( -11592841444168322 + T \)
$73$ \( -100714945072821154 + T \)
$79$ \( 126856003456085902 + T \)
$83$ \( -367224638997840874 + T \)
$89$ \( T \)
$97$ \( 1519865703804919214 + T \)
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