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

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

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