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

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

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 \(-10\) \(260\) \(1250\) \(1700\) \(-\) \(q+(-5-\beta )q^{2}+(130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)