Properties

Label 10.6.b
Level 10
Weight 6
Character orbit b
Rep. character \(\chi_{10}(9,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 10.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(10, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 6 2 4
Eisenstein series 4 0 4

Trace form

\( 2q - 32q^{4} + 110q^{5} - 112q^{6} + 94q^{9} + O(q^{10}) \) \( 2q - 32q^{4} + 110q^{5} - 112q^{6} + 94q^{9} - 80q^{10} - 296q^{11} + 1264q^{14} - 280q^{15} + 512q^{16} - 4440q^{19} - 1760q^{20} + 4424q^{21} + 1792q^{24} + 5850q^{25} - 5472q^{26} + 540q^{29} - 6160q^{30} - 4096q^{31} + 16384q^{34} + 3160q^{35} - 1504q^{36} - 19152q^{39} + 1280q^{40} - 4796q^{41} + 4736q^{44} + 5170q^{45} + 9968q^{46} - 16314q^{49} - 8800q^{50} + 57344q^{51} - 32480q^{54} - 16280q^{55} - 20224q^{56} + 79480q^{59} + 4480q^{60} - 84596q^{61} - 8192q^{64} - 13680q^{65} + 16576q^{66} + 34888q^{69} + 69520q^{70} - 8496q^{71} - 34976q^{74} - 30800q^{75} + 71040q^{76} - 70560q^{79} + 28160q^{80} - 90838q^{81} - 70784q^{84} + 40960q^{85} - 18352q^{86} + 170420q^{89} - 3760q^{90} + 216144q^{91} - 85456q^{94} - 244200q^{95} - 28672q^{96} - 13912q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
10.6.b.a \(2\) \(1.604\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(110\) \(0\) \(q+2iq^{2}+7iq^{3}-2^{4}q^{4}+(55+5i)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 16 T^{2} \)
$3$ \( 1 - 290 T^{2} + 59049 T^{4} \)
$5$ \( 1 - 110 T + 3125 T^{2} \)
$7$ \( 1 - 8650 T^{2} + 282475249 T^{4} \)
$11$ \( ( 1 + 148 T + 161051 T^{2} )^{2} \)
$13$ \( 1 - 274730 T^{2} + 137858491849 T^{4} \)
$17$ \( 1 + 1354590 T^{2} + 2015993900449 T^{4} \)
$19$ \( ( 1 + 2220 T + 2476099 T^{2} )^{2} \)
$23$ \( 1 - 11320170 T^{2} + 41426511213649 T^{4} \)
$29$ \( ( 1 - 270 T + 20511149 T^{2} )^{2} \)
$31$ \( ( 1 + 2048 T + 28629151 T^{2} )^{2} \)
$37$ \( 1 - 119573530 T^{2} + 4808584372417849 T^{4} \)
$41$ \( ( 1 + 2398 T + 115856201 T^{2} )^{2} \)
$43$ \( 1 - 288754450 T^{2} + 21611482313284249 T^{4} \)
$47$ \( 1 - 344584890 T^{2} + 52599132235830049 T^{4} \)
$53$ \( 1 - 827605690 T^{2} + 174887470365513049 T^{4} \)
$59$ \( ( 1 - 39740 T + 714924299 T^{2} )^{2} \)
$61$ \( ( 1 + 42298 T + 844596301 T^{2} )^{2} \)
$67$ \( 1 - 1669968610 T^{2} + 1822837804551761449 T^{4} \)
$71$ \( ( 1 + 4248 T + 1804229351 T^{2} )^{2} \)
$73$ \( 1 - 3239892370 T^{2} + 4297625829703557649 T^{4} \)
$79$ \( ( 1 + 35280 T + 3077056399 T^{2} )^{2} \)
$83$ \( 1 - 7103795010 T^{2} + 15516041187205853449 T^{4} \)
$89$ \( ( 1 - 85210 T + 5584059449 T^{2} )^{2} \)
$97$ \( 1 - 7720618690 T^{2} + 73742412689492826049 T^{4} \)
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