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Properties

Label 2.10.a
Level 2
Weight 10
Character orbit a
Rep. character \(\chi_{2}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 2 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 2.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(2))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim.
\(-\)\(1\)

Trace form

\( q + 16q^{2} - 156q^{3} + 256q^{4} + 870q^{5} - 2496q^{6} - 952q^{7} + 4096q^{8} + 4653q^{9} + O(q^{10}) \) \( q + 16q^{2} - 156q^{3} + 256q^{4} + 870q^{5} - 2496q^{6} - 952q^{7} + 4096q^{8} + 4653q^{9} + 13920q^{10} - 56148q^{11} - 39936q^{12} + 178094q^{13} - 15232q^{14} - 135720q^{15} + 65536q^{16} - 247662q^{17} + 74448q^{18} + 315380q^{19} + 222720q^{20} + 148512q^{21} - 898368q^{22} + 204504q^{23} - 638976q^{24} - 1196225q^{25} + 2849504q^{26} + 2344680q^{27} - 243712q^{28} - 3840450q^{29} - 2171520q^{30} - 1309408q^{31} + 1048576q^{32} + 8759088q^{33} - 3962592q^{34} - 828240q^{35} + 1191168q^{36} + 4307078q^{37} + 5046080q^{38} - 27782664q^{39} + 3563520q^{40} + 1512042q^{41} + 2376192q^{42} + 33670604q^{43} - 14373888q^{44} + 4048110q^{45} + 3272064q^{46} - 10581072q^{47} - 10223616q^{48} - 39447303q^{49} - 19139600q^{50} + 38635272q^{51} + 45592064q^{52} + 16616214q^{53} + 37514880q^{54} - 48848760q^{55} - 3899392q^{56} - 49199280q^{57} - 61447200q^{58} + 112235100q^{59} - 34744320q^{60} - 33197218q^{61} - 20950528q^{62} - 4429656q^{63} + 16777216q^{64} + 154941780q^{65} + 140145408q^{66} - 121372252q^{67} - 63401472q^{68} - 31902624q^{69} - 13251840q^{70} - 387172728q^{71} + 19058688q^{72} + 255240074q^{73} + 68913248q^{74} + 186611100q^{75} + 80737280q^{76} + 53452896q^{77} - 444522624q^{78} + 492101840q^{79} + 57016320q^{80} - 457355079q^{81} + 24192672q^{82} - 457420236q^{83} + 38019072q^{84} - 215465940q^{85} + 538729664q^{86} + 599110200q^{87} - 229982208q^{88} - 31809510q^{89} + 64769760q^{90} - 169545488q^{91} + 52353024q^{92} + 204267648q^{93} - 169297152q^{94} + 274380600q^{95} - 163577856q^{96} - 673532062q^{97} - 631156848q^{98} - 261256644q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.10.a.a \(1\) \(1.030\) \(\Q\) None \(16\) \(-156\) \(870\) \(-952\) \(-\) \(q+2^{4}q^{2}-156q^{3}+2^{8}q^{4}+870q^{5}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 16 T \)
$3$ \( 1 + 156 T + 19683 T^{2} \)
$5$ \( 1 - 870 T + 1953125 T^{2} \)
$7$ \( 1 + 952 T + 40353607 T^{2} \)
$11$ \( 1 + 56148 T + 2357947691 T^{2} \)
$13$ \( 1 - 178094 T + 10604499373 T^{2} \)
$17$ \( 1 + 247662 T + 118587876497 T^{2} \)
$19$ \( 1 - 315380 T + 322687697779 T^{2} \)
$23$ \( 1 - 204504 T + 1801152661463 T^{2} \)
$29$ \( 1 + 3840450 T + 14507145975869 T^{2} \)
$31$ \( 1 + 1309408 T + 26439622160671 T^{2} \)
$37$ \( 1 - 4307078 T + 129961739795077 T^{2} \)
$41$ \( 1 - 1512042 T + 327381934393961 T^{2} \)
$43$ \( 1 - 33670604 T + 502592611936843 T^{2} \)
$47$ \( 1 + 10581072 T + 1119130473102767 T^{2} \)
$53$ \( 1 - 16616214 T + 3299763591802133 T^{2} \)
$59$ \( 1 - 112235100 T + 8662995818654939 T^{2} \)
$61$ \( 1 + 33197218 T + 11694146092834141 T^{2} \)
$67$ \( 1 + 121372252 T + 27206534396294947 T^{2} \)
$71$ \( 1 + 387172728 T + 45848500718449031 T^{2} \)
$73$ \( 1 - 255240074 T + 58871586708267913 T^{2} \)
$79$ \( 1 - 492101840 T + 119851595982618319 T^{2} \)
$83$ \( 1 + 457420236 T + 186940255267540403 T^{2} \)
$89$ \( 1 + 31809510 T + 350356403707485209 T^{2} \)
$97$ \( 1 + 673532062 T + 760231058654565217 T^{2} \)
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