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: \(3.8417159028\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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.

Atkin-Lehner signs

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

Hecke kernels

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