Properties

Label 20.6.c
Level 20
Weight 6
Character orbit c
Rep. character \(\chi_{20}(9,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 20.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 18 2 16
Cusp forms 12 2 10
Eisenstein series 6 0 6

Trace form

\( 2q - 10q^{5} + 238q^{9} + O(q^{10}) \) \( 2q - 10q^{5} + 238q^{9} - 200q^{11} - 1240q^{15} + 4488q^{19} - 2728q^{21} - 6150q^{25} + 15708q^{29} - 4288q^{31} - 13640q^{35} + 16368q^{39} - 14828q^{41} - 1190q^{45} + 3606q^{49} + 21824q^{51} + 1000q^{55} - 51944q^{59} - 6116q^{61} + 81840q^{65} - 76136q^{69} + 75216q^{71} + 12400q^{75} - 159456q^{79} - 31942q^{81} + 109120q^{85} + 1652q^{89} + 180048q^{91} - 22440q^{95} - 23800q^{99} + O(q^{100}) \)

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.c.a \(2\) \(3.208\) \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(-10\) \(0\) \(q-\beta q^{3}+(-5-5\beta )q^{5}-11\beta q^{7}+119q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 362 T^{2} + 59049 T^{4} \)
$5$ \( 1 + 10 T + 3125 T^{2} \)
$7$ \( 1 - 18610 T^{2} + 282475249 T^{4} \)
$11$ \( ( 1 + 100 T + 161051 T^{2} )^{2} \)
$13$ \( 1 - 202442 T^{2} + 137858491849 T^{4} \)
$17$ \( 1 - 1879458 T^{2} + 2015993900449 T^{4} \)
$19$ \( ( 1 - 2244 T + 2476099 T^{2} )^{2} \)
$23$ \( 1 - 1185810 T^{2} + 41426511213649 T^{4} \)
$29$ \( ( 1 - 7854 T + 20511149 T^{2} )^{2} \)
$31$ \( ( 1 + 2144 T + 28629151 T^{2} )^{2} \)
$37$ \( 1 - 30515770 T^{2} + 4808584372417849 T^{4} \)
$41$ \( ( 1 + 7414 T + 115856201 T^{2} )^{2} \)
$43$ \( 1 + 21442214 T^{2} + 21611482313284249 T^{4} \)
$47$ \( 1 - 369731298 T^{2} + 52599132235830049 T^{4} \)
$53$ \( 1 - 248174170 T^{2} + 174887470365513049 T^{4} \)
$59$ \( ( 1 + 25972 T + 714924299 T^{2} )^{2} \)
$61$ \( ( 1 + 3058 T + 844596301 T^{2} )^{2} \)
$67$ \( 1 + 755362070 T^{2} + 1822837804551761449 T^{4} \)
$71$ \( ( 1 - 37608 T + 1804229351 T^{2} )^{2} \)
$73$ \( 1 - 3569749522 T^{2} + 4297625829703557649 T^{4} \)
$79$ \( ( 1 + 79728 T + 3077056399 T^{2} )^{2} \)
$83$ \( 1 - 7612675530 T^{2} + 15516041187205853449 T^{4} \)
$89$ \( ( 1 - 826 T + 5584059449 T^{2} )^{2} \)
$97$ \( 1 - 15761405890 T^{2} + 73742412689492826049 T^{4} \)
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