Properties

Label 20.6.e
Level 20
Weight 6
Character orbit e
Rep. character \(\chi_{20}(3,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 26
Newform subspaces 2
Sturm bound 18
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 20.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(20, [\chi])\).

Total New Old
Modular forms 34 34 0
Cusp forms 26 26 0
Eisenstein series 8 8 0

Trace form

\( 26q - 2q^{2} - 4q^{5} - 184q^{6} + 244q^{8} + O(q^{10}) \) \( 26q - 2q^{2} - 4q^{5} - 184q^{6} + 244q^{8} + 566q^{10} - 1280q^{12} + 118q^{13} + 1976q^{16} + 1006q^{17} - 3246q^{18} - 1364q^{20} + 1632q^{21} - 2440q^{22} - 7794q^{25} + 6836q^{26} + 5920q^{28} + 8600q^{30} + 17608q^{32} + 10400q^{33} - 27908q^{36} - 9414q^{37} - 22160q^{38} - 31444q^{40} - 9648q^{41} - 39400q^{42} + 27886q^{45} + 29416q^{46} + 108160q^{48} + 114186q^{50} + 38476q^{52} - 58982q^{53} - 85984q^{56} + 40320q^{57} - 183672q^{58} - 263840q^{60} + 96152q^{61} - 109400q^{62} - 68198q^{65} + 186000q^{66} + 313988q^{68} + 364240q^{70} + 309828q^{72} + 39298q^{73} - 297600q^{76} - 53280q^{77} - 586200q^{78} - 467824q^{80} - 184842q^{81} - 458744q^{82} - 27578q^{85} + 545416q^{86} + 690080q^{88} + 945366q^{90} + 576800q^{92} + 182240q^{93} - 841984q^{96} + 129426q^{97} - 1036906q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.6.e.a \(2\) \(3.208\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(8\) \(0\) \(76\) \(0\) \(q+(4+4i)q^{2}+2^{5}iq^{4}+(38+41i)q^{5}+\cdots\)
20.6.e.b \(24\) \(3.208\) None \(-10\) \(0\) \(-80\) \(0\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 8 T + 32 T^{2} \))
$3$ (\( 1 + 59049 T^{4} \))
$5$ (\( 1 - 76 T + 3125 T^{2} \))
$7$ (\( 1 + 282475249 T^{4} \))
$11$ (\( ( 1 - 161051 T^{2} )^{2} \))
$13$ (\( ( 1 - 1194 T + 371293 T^{2} )( 1 - 244 T + 371293 T^{2} ) \))
$17$ (\( ( 1 - 808 T + 1419857 T^{2} )( 1 + 2242 T + 1419857 T^{2} ) \))
$19$ (\( ( 1 + 2476099 T^{2} )^{2} \))
$23$ (\( 1 + 41426511213649 T^{4} \))
$29$ (\( ( 1 - 2950 T + 20511149 T^{2} )( 1 + 2950 T + 20511149 T^{2} ) \))
$31$ (\( ( 1 - 28629151 T^{2} )^{2} \))
$37$ (\( ( 1 + 11292 T + 69343957 T^{2} )( 1 + 12242 T + 69343957 T^{2} ) \))
$41$ (\( ( 1 - 4952 T + 115856201 T^{2} )^{2} \))
$43$ (\( 1 + 21611482313284249 T^{4} \))
$47$ (\( 1 + 52599132235830049 T^{4} \))
$53$ (\( ( 1 - 40244 T + 418195493 T^{2} )( 1 - 7294 T + 418195493 T^{2} ) \))
$59$ (\( ( 1 + 714924299 T^{2} )^{2} \))
$61$ (\( ( 1 + 54948 T + 844596301 T^{2} )^{2} \))
$67$ (\( 1 + 1822837804551761449 T^{4} \))
$71$ (\( ( 1 - 1804229351 T^{2} )^{2} \))
$73$ (\( ( 1 - 20144 T + 2073071593 T^{2} )( 1 + 88806 T + 2073071593 T^{2} ) \))
$79$ (\( ( 1 + 3077056399 T^{2} )^{2} \))
$83$ (\( 1 + 15516041187205853449 T^{4} \))
$89$ (\( ( 1 - 51050 T + 5584059449 T^{2} )( 1 + 51050 T + 5584059449 T^{2} ) \))
$97$ (\( ( 1 - 160808 T + 8587340257 T^{2} )( 1 + 92142 T + 8587340257 T^{2} ) \))
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