Properties

Label 35.23.c.a
Level $35$
Weight $23$
Character orbit 35.c
Self dual yes
Analytic conductor $107.348$
Analytic rank $0$
Dimension $1$
CM discriminant -35
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 23 \)
Character orbit: \([\chi]\) \(=\) 35.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(107.347602195\)
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

\(f(q)\) \(=\) \( q - 341351q^{3} + 4194304q^{4} - 48828125q^{5} + 1977326743q^{7} + 85139445592q^{9} + O(q^{10}) \) \( q - 341351q^{3} + 4194304q^{4} - 48828125q^{5} + 1977326743q^{7} + 85139445592q^{9} + 354730232987q^{11} - 1431729864704q^{12} + 1431532005269q^{13} + 16667529296875q^{15} + 17592186044416q^{16} + 66547133948621q^{17} - 204800000000000q^{20} - 674962461049793q^{21} + 2384185791015625q^{25} - 18350478813683033q^{27} + 8293509467471872q^{28} + 23774726872835423q^{29} - 121087519760345437q^{33} - 96549157373046875q^{35} + 357100717204307968q^{36} - 488654881530578419q^{39} + 1487846435138306048q^{44} - 4157199491796875000q^{45} - 2606499276897091519q^{47} - 6005110298447446016q^{48} + 3909821048582988049q^{49} - 22715930720495726971q^{51} + 6004280415827787776q^{52} - 17320812157568359375q^{55} + 69908684800000000000q^{60} + 168348502653255066856q^{63} + 73786976294838206464q^{64} - 69899023694775390625q^{65} + 279118910109236854784q^{68} - 71331542064478634398q^{71} + 331277992533217385534q^{73} - 813844203948974609375q^{75} + 701417576235815871341q^{77} - 488366004075197305357q^{79} - 858993459200000000000q^{80} + 3592188276329752704055q^{81} + 743012515936423630214q^{83} - 2830997750230990979072q^{84} - 3249371774835009765625q^{85} - 8115526792769244476473q^{87} + 2830606517478810608867q^{91} + 2964986501937961437701q^{97} + 30201535371234170143304q^{99} + O(q^{100}) \)

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 −341351. 4.19430e6 −4.88281e7 0 1.97733e9 0 8.51394e10 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 35.23.c.a 1
5.b even 2 1 35.23.c.b yes 1
7.b odd 2 1 35.23.c.b yes 1
35.c odd 2 1 CM 35.23.c.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.23.c.a 1 1.a even 1 1 trivial
35.23.c.a 1 35.c odd 2 1 CM
35.23.c.b yes 1 5.b even 2 1
35.23.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 \(S_{23}^{\mathrm{new}}(35, [\chi])\):

\( T_{2} \)
\( T_{3} + 341351 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 341351 + T \)
$5$ \( 48828125 + T \)
$7$ \( -1977326743 + T \)
$11$ \( -354730232987 + T \)
$13$ \( -1431532005269 + T \)
$17$ \( -66547133948621 + T \)
$19$ \( T \)
$23$ \( T \)
$29$ \( -23774726872835423 + T \)
$31$ \( T \)
$37$ \( T \)
$41$ \( T \)
$43$ \( T \)
$47$ \( 2606499276897091519 + T \)
$53$ \( T \)
$59$ \( T \)
$61$ \( T \)
$67$ \( T \)
$71$ \( 71331542064478634398 + T \)
$73$ \( -\)\(33\!\cdots\!34\)\( + T \)
$79$ \( \)\(48\!\cdots\!57\)\( + T \)
$83$ \( -\)\(74\!\cdots\!14\)\( + T \)
$89$ \( T \)
$97$ \( -\)\(29\!\cdots\!01\)\( + T \)
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