↑

Properties

Label 5.16
Level 5
Weight 16
Dimension 11
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 32
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(32\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(5))\).

Total New Old
Modular forms 17 13 4
Cusp forms 13 11 2
Eisenstein series 4 2 2

Trace form

\( 11 q - 306 q^{2} + 5258 q^{3} + 21372 q^{4} - 316475 q^{5} + 1404112 q^{6} - 4326106 q^{7} + 3018600 q^{8} + 9539023 q^{9} + O(q^{10}) \) \( 11 q - 306 q^{2} + 5258 q^{3} + 21372 q^{4} - 316475 q^{5} + 1404112 q^{6} - 4326106 q^{7} + 3018600 q^{8} + 9539023 q^{9} - 72805450 q^{10} + 12748872 q^{11} + 258612544 q^{12} - 248058342 q^{13} - 409515816 q^{14} + 158837150 q^{15} + 2661514416 q^{16} - 4320523806 q^{17} + 5282035958 q^{18} - 4406005140 q^{19} + 4031566300 q^{20} - 3113068548 q^{21} - 12567256712 q^{22} + 710131458 q^{23} - 3181281120 q^{24} + 48768456875 q^{25} + 30587013492 q^{26} - 147114144100 q^{27} - 151565090608 q^{28} + 522055465290 q^{29} + 29616626800 q^{30} - 344725724428 q^{31} - 641389196256 q^{32} + 783433600816 q^{33} + 459268230844 q^{34} + 974736318050 q^{35} - 3342628997284 q^{36} - 821087058806 q^{37} + 1685828089800 q^{38} + 4671561206756 q^{39} + 1844686977000 q^{40} - 7226089147278 q^{41} - 9276717500112 q^{42} + 2542794692658 q^{43} + 21890529696144 q^{44} + 4593752029825 q^{45} - 21778907869128 q^{46} - 13697280311106 q^{47} + 3181970775808 q^{48} + 28492655413307 q^{49} + 21826542288750 q^{50} - 31986428165468 q^{51} - 46582060820456 q^{52} + 15422281085058 q^{53} + 39365548850560 q^{54} + 24257706615800 q^{55} - 48673824272640 q^{56} - 43954185568600 q^{57} + 55409886578900 q^{58} + 35140265194380 q^{59} + 18895349864800 q^{60} - 12147566704578 q^{61} - 62750540178912 q^{62} - 52433003461242 q^{63} + 43447613861312 q^{64} - 55849919931850 q^{65} + 151432330939424 q^{66} + 184267352518694 q^{67} - 114413077226808 q^{68} - 256956884358204 q^{69} - 53511139271400 q^{70} - 115608426661428 q^{71} + 453115808123400 q^{72} + 121189601096058 q^{73} - 420532055448636 q^{74} - 328873641733750 q^{75} + 734761873255120 q^{76} + 217227988844688 q^{77} - 536216138865584 q^{78} - 594447578673160 q^{79} - 229910502827600 q^{80} + 1235121491165551 q^{81} + 823442138616188 q^{82} + 19801694051058 q^{83} - 1890543750974496 q^{84} - 281234850022450 q^{85} + 655007338619232 q^{86} + 1316818252719500 q^{87} - 593233866448800 q^{88} - 1001177846740530 q^{89} - 743214187032850 q^{90} + 2406085851856732 q^{91} - 594285852866256 q^{92} - 343159219528584 q^{93} + 964881278873224 q^{94} - 401835581963500 q^{95} - 2694801441071488 q^{96} - 1472059883554406 q^{97} + 1919570413071342 q^{98} + 1690650292479896 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(5))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5.16.a \(\chi_{5}(1, \cdot)\) 5.16.a.a 2 1
5.16.a.b 3
5.16.b \(\chi_{5}(4, \cdot)\) 5.16.b.a 6 1

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)