Properties

Label 6.10
Level 6
Weight 10
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 20
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(6))\).

Total New Old
Modular forms 11 1 10
Cusp forms 7 1 6
Eisenstein series 4 0 4

Trace form

\( q - 16q^{2} + 81q^{3} + 256q^{4} + 2694q^{5} - 1296q^{6} - 3544q^{7} - 4096q^{8} + 6561q^{9} + O(q^{10}) \) \( q - 16q^{2} + 81q^{3} + 256q^{4} + 2694q^{5} - 1296q^{6} - 3544q^{7} - 4096q^{8} + 6561q^{9} - 43104q^{10} + 29580q^{11} + 20736q^{12} - 44818q^{13} + 56704q^{14} + 218214q^{15} + 65536q^{16} - 101934q^{17} - 104976q^{18} - 895084q^{19} + 689664q^{20} - 287064q^{21} - 473280q^{22} - 1113000q^{23} - 331776q^{24} + 5304511q^{25} + 717088q^{26} + 531441q^{27} - 907264q^{28} - 2357346q^{29} - 3491424q^{30} + 175808q^{31} - 1048576q^{32} + 2395980q^{33} + 1630944q^{34} - 9547536q^{35} + 1679616q^{36} - 2919418q^{37} + 14321344q^{38} - 3630258q^{39} - 11034624q^{40} + 26218794q^{41} + 4593024q^{42} - 18762964q^{43} + 7572480q^{44} + 17675334q^{45} + 17808000q^{46} - 20966160q^{47} + 5308416q^{48} - 27793671q^{49} - 84872176q^{50} - 8256654q^{51} - 11473408q^{52} + 57251574q^{53} - 8503056q^{54} + 79688520q^{55} + 14516224q^{56} - 72501804q^{57} + 37717536q^{58} + 33587580q^{59} + 55862784q^{60} + 82260830q^{61} - 2812928q^{62} - 23252184q^{63} + 16777216q^{64} - 120739692q^{65} - 38335680q^{66} - 188455804q^{67} - 26095104q^{68} - 90153000q^{69} + 152760576q^{70} + 80924040q^{71} - 26873856q^{72} - 236140918q^{73} + 46710688q^{74} + 429665391q^{75} - 229141504q^{76} - 104831520q^{77} + 58084128q^{78} + 526909808q^{79} + 176553984q^{80} + 43046721q^{81} - 419500704q^{82} + 18346452q^{83} - 73488384q^{84} - 274610196q^{85} + 300207424q^{86} - 190945026q^{87} - 121159680q^{88} + 690643098q^{89} - 282805344q^{90} + 158834992q^{91} - 284928000q^{92} + 14240448q^{93} + 335458560q^{94} - 2411356296q^{95} - 84934656q^{96} - 438251038q^{97} + 444698736q^{98} + 194074380q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6.10.a \(\chi_{6}(1, \cdot)\) 6.10.a.a 1 1

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 16 T \)
$3$ \( 1 - 81 T \)
$5$ \( 1 - 2694 T + 1953125 T^{2} \)
$7$ \( 1 + 3544 T + 40353607 T^{2} \)
$11$ \( 1 - 29580 T + 2357947691 T^{2} \)
$13$ \( 1 + 44818 T + 10604499373 T^{2} \)
$17$ \( 1 + 101934 T + 118587876497 T^{2} \)
$19$ \( 1 + 895084 T + 322687697779 T^{2} \)
$23$ \( 1 + 1113000 T + 1801152661463 T^{2} \)
$29$ \( 1 + 2357346 T + 14507145975869 T^{2} \)
$31$ \( 1 - 175808 T + 26439622160671 T^{2} \)
$37$ \( 1 + 2919418 T + 129961739795077 T^{2} \)
$41$ \( 1 - 26218794 T + 327381934393961 T^{2} \)
$43$ \( 1 + 18762964 T + 502592611936843 T^{2} \)
$47$ \( 1 + 20966160 T + 1119130473102767 T^{2} \)
$53$ \( 1 - 57251574 T + 3299763591802133 T^{2} \)
$59$ \( 1 - 33587580 T + 8662995818654939 T^{2} \)
$61$ \( 1 - 82260830 T + 11694146092834141 T^{2} \)
$67$ \( 1 + 188455804 T + 27206534396294947 T^{2} \)
$71$ \( 1 - 80924040 T + 45848500718449031 T^{2} \)
$73$ \( 1 + 236140918 T + 58871586708267913 T^{2} \)
$79$ \( 1 - 526909808 T + 119851595982618319 T^{2} \)
$83$ \( 1 - 18346452 T + 186940255267540403 T^{2} \)
$89$ \( 1 - 690643098 T + 350356403707485209 T^{2} \)
$97$ \( 1 + 438251038 T + 760231058654565217 T^{2} \)
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