Properties

Label 20.10.e
Level 20
Weight 10
Character orbit e
Rep. character \(\chi_{20}(3,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 50
Newform subspaces 2
Sturm bound 30
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
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: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(20, [\chi])\).

Total New Old
Modular forms 58 58 0
Cusp forms 50 50 0
Eisenstein series 8 8 0

Trace form

\( 50q - 2q^{2} - 4q^{5} + 6152q^{6} - 716q^{8} + O(q^{10}) \) \( 50q - 2q^{2} - 4q^{5} + 6152q^{6} - 716q^{8} + 11446q^{10} - 155360q^{12} - 86162q^{13} + 3000q^{16} - 509994q^{17} - 679086q^{18} - 334324q^{20} - 634176q^{21} + 3176920q^{22} + 4304406q^{25} - 11222732q^{26} + 12731840q^{28} + 15498680q^{30} - 29092792q^{32} - 2488000q^{33} + 44773372q^{36} - 1602814q^{37} - 26115120q^{38} - 55995604q^{40} - 3634000q^{41} + 82830200q^{42} + 31366486q^{45} - 92534488q^{46} + 46448320q^{48} - 54429014q^{50} + 88926156q^{52} - 195634782q^{53} - 177356448q^{56} + 62365440q^{57} + 82723048q^{58} + 166923520q^{60} + 180242200q^{61} - 292810200q^{62} + 64634162q^{65} + 614341200q^{66} - 289868412q^{68} - 203227600q^{70} + 930217668q^{72} + 504789018q^{73} - 1061841600q^{76} - 277316160q^{77} + 49362600q^{78} + 210150736q^{80} - 1707948546q^{81} - 591442904q^{82} + 1383913502q^{85} - 874588728q^{86} + 865939360q^{88} + 1779829206q^{90} - 1106673600q^{92} - 2554477120q^{93} + 1870685312q^{96} + 3440322826q^{97} - 3885590026q^{98} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.10.e.a \(2\) \(10.301\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(-32\) \(0\) \(1436\) \(0\) \(q+(-2^{4}-2^{4}i)q^{2}+2^{9}iq^{4}+(718+\cdots)q^{5}+\cdots\)
20.10.e.b \(48\) \(10.301\) None \(30\) \(0\) \(-1440\) \(0\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 32 T + 512 T^{2} \))
$3$ (\( 1 + 387420489 T^{4} \))
$5$ (\( 1 - 1436 T + 1953125 T^{2} \))
$7$ (\( 1 + 1628413597910449 T^{4} \))
$11$ (\( ( 1 - 2357947691 T^{2} )^{2} \))
$13$ (\( ( 1 + 112806 T + 10604499373 T^{2} )( 1 + 172316 T + 10604499373 T^{2} ) \))
$17$ (\( ( 1 + 407992 T + 118587876497 T^{2} )( 1 + 554882 T + 118587876497 T^{2} ) \))
$19$ (\( ( 1 + 322687697779 T^{2} )^{2} \))
$23$ (\( 1 + \)\(32\!\cdots\!69\)\( T^{4} \))
$29$ (\( ( 1 - 7314710 T + 14507145975869 T^{2} )( 1 + 7314710 T + 14507145975869 T^{2} ) \))
$31$ (\( ( 1 - 26439622160671 T^{2} )^{2} \))
$37$ (\( ( 1 + 1923372 T + 129961739795077 T^{2} )( 1 + 22718882 T + 129961739795077 T^{2} ) \))
$41$ (\( ( 1 - 7561912 T + 327381934393961 T^{2} )^{2} \))
$43$ (\( 1 + \)\(25\!\cdots\!49\)\( T^{4} \))
$47$ (\( 1 + \)\(12\!\cdots\!89\)\( T^{4} \))
$53$ (\( ( 1 - 68323684 T + 3299763591802133 T^{2} )( 1 + 92363026 T + 3299763591802133 T^{2} ) \))
$59$ (\( ( 1 + 8662995818654939 T^{2} )^{2} \))
$61$ (\( ( 1 - 216178092 T + 11694146092834141 T^{2} )^{2} \))
$67$ (\( 1 + \)\(74\!\cdots\!09\)\( T^{4} \))
$71$ (\( ( 1 - 45848500718449031 T^{2} )^{2} \))
$73$ (\( ( 1 - 483419504 T + 58871586708267913 T^{2} )( 1 - 42331194 T + 58871586708267913 T^{2} ) \))
$79$ (\( ( 1 + 119851595982618319 T^{2} )^{2} \))
$83$ (\( 1 + \)\(34\!\cdots\!09\)\( T^{4} \))
$89$ (\( ( 1 - 1125568310 T + 350356403707485209 T^{2} )( 1 + 1125568310 T + 350356403707485209 T^{2} ) \))
$97$ (\( ( 1 + 1016663992 T + 760231058654565217 T^{2} )( 1 + 1416798702 T + 760231058654565217 T^{2} ) \))
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