Properties

Label 5.12.a.a
Level 5
Weight 12
Character orbit 5.a
Self dual yes
Analytic conductor 3.842
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.84171590280\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q + 34q^{2} - 792q^{3} - 892q^{4} + 3125q^{5} - 26928q^{6} - 17556q^{7} - 99960q^{8} + 450117q^{9} + O(q^{10}) \) \( q + 34q^{2} - 792q^{3} - 892q^{4} + 3125q^{5} - 26928q^{6} - 17556q^{7} - 99960q^{8} + 450117q^{9} + 106250q^{10} - 468788q^{11} + 706464q^{12} - 374042q^{13} - 596904q^{14} - 2475000q^{15} - 1571824q^{16} - 3724286q^{17} + 15303978q^{18} - 379460q^{19} - 2787500q^{20} + 13904352q^{21} - 15938792q^{22} - 32458092q^{23} + 79168320q^{24} + 9765625q^{25} - 12717428q^{26} - 216192240q^{27} + 15659952q^{28} + 69696710q^{29} - 84150000q^{30} + 171448632q^{31} + 151276064q^{32} + 371280096q^{33} - 126625724q^{34} - 54862500q^{35} - 401504364q^{36} - 291340546q^{37} - 12901640q^{38} + 296241264q^{39} - 312375000q^{40} + 191343242q^{41} + 472747968q^{42} - 1759857392q^{43} + 418158896q^{44} + 1406615625q^{45} - 1103575128q^{46} + 1623469924q^{47} + 1244884608q^{48} - 1669113607q^{49} + 332031250q^{50} + 2949634512q^{51} + 333645464q^{52} - 644888642q^{53} - 7350536160q^{54} - 1464962500q^{55} + 1754897760q^{56} + 300532320q^{57} + 2369688140q^{58} + 925569220q^{59} + 2207700000q^{60} - 10898589338q^{61} + 5829253488q^{62} - 7902254052q^{63} + 8362481728q^{64} - 1168881250q^{65} + 12623523264q^{66} + 3795674064q^{67} + 3322063112q^{68} + 25706808864q^{69} - 1865325000q^{70} - 22966943728q^{71} - 44993695320q^{72} + 9880820458q^{73} - 9905578564q^{74} - 7734375000q^{75} + 338478320q^{76} + 8230042128q^{77} + 10072202976q^{78} - 20768886240q^{79} - 4911950000q^{80} + 91487377881q^{81} + 6505670228q^{82} + 3204862008q^{83} - 12402681984q^{84} - 11638393750q^{85} - 59835151328q^{86} - 55199794320q^{87} + 46860048480q^{88} + 63176321130q^{89} + 47824931250q^{90} + 6566681352q^{91} + 28952618064q^{92} - 135787316544q^{93} + 55197977416q^{94} - 1185812500q^{95} - 119810642688q^{96} + 126494473874q^{97} - 56749862638q^{98} - 211009448196q^{99} + O(q^{100}) \)

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
34.0000 −792.000 −892.000 3125.00 −26928.0 −17556.0 −99960.0 450117. 106250.
\(n\): 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 5.12.a.a 1
3.b odd 2 1 45.12.a.a 1
4.b odd 2 1 80.12.a.f 1
5.b even 2 1 25.12.a.a 1
5.c odd 4 2 25.12.b.a 2
7.b odd 2 1 245.12.a.a 1
15.d odd 2 1 225.12.a.e 1
15.e even 4 2 225.12.b.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5.12.a.a 1 1.a even 1 1 trivial
25.12.a.a 1 5.b even 2 1
25.12.b.a 2 5.c odd 4 2
45.12.a.a 1 3.b odd 2 1
80.12.a.f 1 4.b odd 2 1
225.12.a.e 1 15.d odd 2 1
225.12.b.c 2 15.e even 4 2
245.12.a.a 1 7.b odd 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 34 \) acting on \(S_{12}^{\mathrm{new}}(\Gamma_0(5))\).