Properties

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

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
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

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

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