Properties

Label 5.10
Level 5
Weight 10
Dimension 7
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 20
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(20\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(5))\).

Total New Old
Modular forms 11 9 2
Cusp forms 7 7 0
Eisenstein series 4 2 2

Trace form

\( 7q - 18q^{2} + 146q^{3} - 772q^{4} + 1765q^{5} - 1616q^{6} + 5942q^{7} - 12600q^{8} + 7447q^{9} + O(q^{10}) \) \( 7q - 18q^{2} + 146q^{3} - 772q^{4} + 1765q^{5} - 1616q^{6} + 5942q^{7} - 12600q^{8} + 7447q^{9} - 70410q^{10} + 87744q^{11} + 227152q^{12} - 914q^{13} - 898824q^{14} - 162970q^{15} + 1487152q^{16} + 907662q^{17} - 1008394q^{18} - 1942140q^{19} - 2369780q^{20} + 4125084q^{21} + 4083944q^{22} - 1581774q^{23} - 6189120q^{24} - 166025q^{25} + 4242804q^{26} + 313100q^{27} + 3305504q^{28} - 3002310q^{29} - 192320q^{30} - 12339596q^{31} - 4067808q^{32} + 717232q^{33} + 46355196q^{34} + 12041090q^{35} - 41602468q^{36} - 36053298q^{37} + 3821400q^{38} + 35312564q^{39} + 26103400q^{40} - 32689566q^{41} - 61126176q^{42} + 46492906q^{43} + 15517776q^{44} + 61482805q^{45} - 12598376q^{46} + 22853022q^{47} - 38239424q^{48} - 56125957q^{49} - 157123650q^{50} + 29384884q^{51} + 139262232q^{52} + 703446q^{53} + 43238560q^{54} + 16962880q^{55} + 304607520q^{56} + 87911000q^{57} - 231081500q^{58} - 601010220q^{59} - 228876560q^{60} + 131659494q^{61} + 331039104q^{62} + 198326886q^{63} - 78224192q^{64} + 328241930q^{65} + 449606528q^{66} - 45604738q^{67} - 265631256q^{68} - 440502636q^{69} - 762351960q^{70} - 244710276q^{71} - 139728600q^{72} + 533029126q^{73} + 1816209636q^{74} + 716270450q^{75} - 814046160q^{76} - 996146736q^{77} - 794572208q^{78} - 626125160q^{79} + 665853040q^{80} - 829831493q^{81} - 268068116q^{82} + 1664055066q^{83} + 2497474656q^{84} + 1224156090q^{85} - 2537118336q^{86} - 523405300q^{87} - 368023200q^{88} - 772550730q^{89} - 1894205170q^{90} + 663161404q^{91} - 700560288q^{92} - 31047288q^{93} + 2263426056q^{94} + 1649929100q^{95} + 1804123904q^{96} + 618891222q^{97} - 621046626q^{98} - 2383526176q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.10.a \(\chi_{5}(1, \cdot)\) 5.10.a.a 1 1
5.10.a.b 2
5.10.b \(\chi_{5}(4, \cdot)\) 5.10.b.a 4 1