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Properties

Label 5.10.a
Level 5
Weight 10
Character orbit a
Rep. character \(\chi_{5}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 5
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 5.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(5))\).

Total New Old
Modular forms 5 3 2
Cusp forms 3 3 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.

\(5\)Dim.
\(+\)\(1\)
\(-\)\(2\)

Trace form

\( 3q - 18q^{2} + 146q^{3} + 596q^{4} + 625q^{5} - 4424q^{6} + 5942q^{7} - 12600q^{8} - 4181q^{9} + O(q^{10}) \) \( 3q - 18q^{2} + 146q^{3} + 596q^{4} + 625q^{5} - 4424q^{6} + 5942q^{7} - 12600q^{8} - 4181q^{9} - 1250q^{10} - 22224q^{11} + 227152q^{12} - 914q^{13} - 474288q^{14} + 233750q^{15} - 144112q^{16} + 907662q^{17} - 1008394q^{18} - 1305260q^{19} + 932500q^{20} + 601116q^{21} + 4083944q^{22} - 1581774q^{23} - 3754080q^{24} + 1171875q^{25} - 2375964q^{26} + 313100q^{27} + 3305504q^{28} + 529410q^{29} - 3905000q^{30} - 1751884q^{31} - 4067808q^{32} + 717232q^{33} + 19920572q^{34} - 1588750q^{35} + 14797508q^{36} - 36053298q^{37} + 3821400q^{38} + 33625748q^{39} - 17475000q^{40} - 15901014q^{41} - 61126176q^{42} + 46492906q^{43} - 5121168q^{44} + 5745625q^{45} + 48651696q^{46} + 22853022q^{47} - 38239424q^{48} - 9204929q^{49} - 7031250q^{50} - 54632204q^{51} + 139262232q^{52} + 703446q^{53} - 72617360q^{54} + 43870000q^{55} - 10570560q^{56} + 87911000q^{57} - 231081500q^{58} - 140181180q^{59} + 78130000q^{60} - 228831074q^{61} + 331039104q^{62} + 198326886q^{63} - 213219264q^{64} + 144346250q^{65} + 430656992q^{66} - 45604738q^{67} - 265631256q^{68} - 153977772q^{69} - 254010000q^{70} - 197098404q^{71} - 139728600q^{72} + 533029126q^{73} + 639347892q^{74} + 57031250q^{75} + 354443280q^{76} - 996146736q^{77} - 794572208q^{78} + 101918360q^{79} - 299990000q^{80} - 486443657q^{81} - 268068116q^{82} + 1664055066q^{83} + 1378576512q^{84} - 51263750q^{85} - 161213784q^{86} - 523405300q^{87} - 368023200q^{88} + 810150030q^{89} - 697116250q^{90} + 189838876q^{91} - 700560288q^{92} - 31047288q^{93} - 1063675648q^{94} + 445137500q^{95} + 1404784256q^{96} + 618891222q^{97} - 621046626q^{98} - 1654739152q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(5))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5
5.10.a.a \(1\) \(2.575\) \(\Q\) None \(-8\) \(-114\) \(-625\) \(4242\) \(+\) \(q-8q^{2}-114q^{3}-448q^{4}-5^{4}q^{5}+\cdots\)
5.10.a.b \(2\) \(2.575\) \(\Q(\sqrt{1009}) \) None \(-10\) \(260\) \(1250\) \(1700\) \(-\) \(q+(-5-\beta )q^{2}+(130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)