Properties

Label 20.10.c
Level 20
Weight 10
Character orbit c
Rep. character \(\chi_{20}(9,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 30
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
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: \(30\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 30 4 26
Cusp forms 24 4 20
Eisenstein series 6 0 6

Trace form

\( 4q + 660q^{5} - 9044q^{9} + O(q^{10}) \) \( 4q + 660q^{5} - 9044q^{9} - 34800q^{11} - 99760q^{15} - 227664q^{19} - 287296q^{21} - 201900q^{25} + 6265656q^{29} + 374464q^{31} - 8114160q^{35} + 23386656q^{39} - 17648136q^{41} - 53241860q^{45} + 144898812q^{49} - 108703552q^{51} - 197954800q^{55} + 438995472q^{59} - 103044472q^{61} - 417315840q^{65} + 1186715008q^{69} - 504081888q^{71} - 1038341600q^{75} + 1794955008q^{79} - 982752124q^{81} - 1447443520q^{85} + 2381318184q^{89} - 811245024q^{91} - 1944906960q^{95} + 2769662000q^{99} + O(q^{100}) \)

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.c.a \(4\) \(10.301\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(660\) \(0\) \(q+\beta _{1}q^{3}+(165+\beta _{1}-\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 34844 T^{2} + 897243462 T^{4} - 13499279518716 T^{6} + 150094635296999121 T^{8} \)
$5$ \( 1 - 660 T + 318750 T^{2} - 1289062500 T^{3} + 3814697265625 T^{4} \)
$7$ \( 1 - 153156620 T^{2} + 9120528185156598 T^{4} - \)\(24\!\cdots\!80\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} \)
$11$ \( ( 1 + 17400 T + 2292818982 T^{2} + 41028289823400 T^{3} + 5559917313492231481 T^{4} )^{2} \)
$13$ \( 1 - 14000436724 T^{2} + 83025702170976147702 T^{4} - \)\(15\!\cdots\!96\)\( T^{6} + \)\(12\!\cdots\!41\)\( T^{8} \)
$17$ \( 1 - 181978394436 T^{2} + \)\(34\!\cdots\!42\)\( T^{4} - \)\(25\!\cdots\!24\)\( T^{6} + \)\(19\!\cdots\!81\)\( T^{8} \)
$19$ \( ( 1 + 113832 T + 402567657014 T^{2} + 36732186013579128 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} )^{2} \)
$23$ \( 1 + 820282526580 T^{2} + \)\(11\!\cdots\!38\)\( T^{4} + \)\(26\!\cdots\!20\)\( T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \)
$29$ \( ( 1 - 3132828 T + 12854589500734 T^{2} - 45448393113289727532 T^{3} + \)\(21\!\cdots\!61\)\( T^{4} )^{2} \)
$31$ \( ( 1 - 187232 T + 40099942836798 T^{2} - 4950343336386752672 T^{3} + \)\(69\!\cdots\!41\)\( T^{4} )^{2} \)
$37$ \( 1 - 462603258659540 T^{2} + \)\(87\!\cdots\!58\)\( T^{4} - \)\(78\!\cdots\!60\)\( T^{6} + \)\(28\!\cdots\!41\)\( T^{8} \)
$41$ \( ( 1 + 8824068 T + 671552976228678 T^{2} + \)\(28\!\cdots\!48\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} )^{2} \)
$43$ \( 1 - 358707990293372 T^{2} + \)\(21\!\cdots\!94\)\( T^{4} - \)\(90\!\cdots\!28\)\( T^{6} + \)\(63\!\cdots\!01\)\( T^{8} \)
$47$ \( 1 - 1037666802860076 T^{2} + \)\(16\!\cdots\!22\)\( T^{4} - \)\(12\!\cdots\!64\)\( T^{6} + \)\(15\!\cdots\!21\)\( T^{8} \)
$53$ \( 1 - 5310844341928340 T^{2} + \)\(28\!\cdots\!78\)\( T^{4} - \)\(57\!\cdots\!60\)\( T^{6} + \)\(11\!\cdots\!21\)\( T^{8} \)
$59$ \( ( 1 - 219497736 T + 28852098295168902 T^{2} - \)\(19\!\cdots\!04\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} )^{2} \)
$61$ \( ( 1 + 51522236 T - 2665246277981394 T^{2} + \)\(60\!\cdots\!76\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} )^{2} \)
$67$ \( 1 - 83417417389239260 T^{2} + \)\(31\!\cdots\!18\)\( T^{4} - \)\(61\!\cdots\!40\)\( T^{6} + \)\(54\!\cdots\!81\)\( T^{8} \)
$71$ \( ( 1 + 252040944 T + 101042798798695246 T^{2} + \)\(11\!\cdots\!64\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} )^{2} \)
$73$ \( 1 - 79546297979572004 T^{2} + \)\(52\!\cdots\!42\)\( T^{4} - \)\(27\!\cdots\!76\)\( T^{6} + \)\(12\!\cdots\!61\)\( T^{8} \)
$79$ \( ( 1 - 897477504 T + 421888354983619742 T^{2} - \)\(10\!\cdots\!76\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} )^{2} \)
$83$ \( 1 - 186261173343564060 T^{2} + \)\(18\!\cdots\!18\)\( T^{4} - \)\(65\!\cdots\!40\)\( T^{6} + \)\(12\!\cdots\!81\)\( T^{8} \)
$89$ \( ( 1 - 1190659092 T + 825013495390166934 T^{2} - \)\(41\!\cdots\!28\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} )^{2} \)
$97$ \( 1 - 899946211039106180 T^{2} + \)\(23\!\cdots\!78\)\( T^{4} - \)\(52\!\cdots\!20\)\( T^{6} + \)\(33\!\cdots\!21\)\( T^{8} \)
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