Properties

Label 5.6.b
Level 5
Weight 6
Character orbit b
Rep. character \(\chi_{5}(4,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 5.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(5, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\( 2q - 24q^{4} - 90q^{5} + 264q^{6} - 306q^{9} + O(q^{10}) \) \( 2q - 24q^{4} - 90q^{5} + 264q^{6} - 306q^{9} - 440q^{10} + 504q^{11} + 792q^{14} + 1320q^{15} - 2528q^{16} - 440q^{19} + 1080q^{20} - 2376q^{21} + 5280q^{24} + 1850q^{25} + 1584q^{26} - 13860q^{29} - 11880q^{30} + 13504q^{31} + 9152q^{34} + 3960q^{35} + 3672q^{36} - 4752q^{39} - 8800q^{40} - 396q^{41} - 6048q^{44} + 13770q^{45} - 32296q^{46} + 26486q^{49} + 39600q^{50} - 27456q^{51} + 23760q^{54} - 22680q^{55} + 15840q^{56} - 49320q^{59} - 15840q^{60} - 11396q^{61} - 25984q^{64} + 7920q^{65} + 66528q^{66} + 96888q^{69} - 35640q^{70} + 106704q^{71} - 185328q^{74} - 118800q^{75} + 5280q^{76} + 103840q^{79} + 113760q^{80} - 145638q^{81} + 28512q^{84} + 45760q^{85} + 5544q^{86} - 19980q^{89} + 67320q^{90} - 14256q^{91} + 139832q^{94} + 19800q^{95} - 164736q^{96} - 77112q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(5, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.6.b.a \(2\) \(0.802\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-90\) \(0\) \(q-\beta q^{2}+3\beta q^{3}-12q^{4}+(-45-5\beta )q^{5}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 20 T^{2} + 1024 T^{4} \)
$3$ \( ( 1 - 24 T + 243 T^{2} )( 1 + 24 T + 243 T^{2} ) \)
$5$ \( 1 + 90 T + 3125 T^{2} \)
$7$ \( 1 - 30050 T^{2} + 282475249 T^{4} \)
$11$ \( ( 1 - 252 T + 161051 T^{2} )^{2} \)
$13$ \( 1 - 728330 T^{2} + 137858491849 T^{4} \)
$17$ \( 1 - 2363810 T^{2} + 2015993900449 T^{4} \)
$19$ \( ( 1 + 220 T + 2476099 T^{2} )^{2} \)
$23$ \( 1 - 6946370 T^{2} + 41426511213649 T^{4} \)
$29$ \( ( 1 + 6930 T + 20511149 T^{2} )^{2} \)
$31$ \( ( 1 - 6752 T + 28629151 T^{2} )^{2} \)
$37$ \( 1 + 56462470 T^{2} + 4808584372417849 T^{4} \)
$41$ \( ( 1 + 198 T + 115856201 T^{2} )^{2} \)
$43$ \( 1 - 293842250 T^{2} + 21611482313284249 T^{4} \)
$47$ \( 1 - 347593490 T^{2} + 52599132235830049 T^{4} \)
$53$ \( 1 - 802472090 T^{2} + 174887470365513049 T^{4} \)
$59$ \( ( 1 + 24660 T + 714924299 T^{2} )^{2} \)
$61$ \( ( 1 + 5698 T + 844596301 T^{2} )^{2} \)
$67$ \( 1 - 795787610 T^{2} + 1822837804551761449 T^{4} \)
$71$ \( ( 1 - 53352 T + 1804229351 T^{2} )^{2} \)
$73$ \( 1 + 883886830 T^{2} + 4297625829703557649 T^{4} \)
$79$ \( ( 1 - 51920 T + 3077056399 T^{2} )^{2} \)
$83$ \( 1 - 4053674810 T^{2} + 15516041187205853449 T^{4} \)
$89$ \( ( 1 + 9990 T + 5584059449 T^{2} )^{2} \)
$97$ \( 1 - 6923133890 T^{2} + 73742412689492826049 T^{4} \)
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