Properties

Label 5.8
Level 5
Weight 8
Dimension 5
Nonzero newspaces 2
Newforms 3
Sturm bound 16
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(5))\).

Total New Old
Modular forms 9 7 2
Cusp forms 5 5 0
Eisenstein series 4 2 2

Trace form

\( 5q + 6q^{2} - 28q^{3} + 188q^{4} + 25q^{5} - 1040q^{6} - 1744q^{7} + 2280q^{8} + 7957q^{9} + O(q^{10}) \) \( 5q + 6q^{2} - 28q^{3} + 188q^{4} + 25q^{5} - 1040q^{6} - 1744q^{7} + 2280q^{8} + 7957q^{9} + 1550q^{10} - 8940q^{11} - 26624q^{12} + 7402q^{13} + 39576q^{14} + 8900q^{15} - 29520q^{16} - 39594q^{17} + 29582q^{18} + 26540q^{19} - 1700q^{20} + 36960q^{21} + 103832q^{22} - 111168q^{23} - 269280q^{24} - 86875q^{25} + 107460q^{26} + 305720q^{27} + 53648q^{28} - 102690q^{29} + 158800q^{30} + 314160q^{31} + 100896q^{32} - 449216q^{33} - 619604q^{34} - 419200q^{35} - 184420q^{36} - 12894q^{37} + 702120q^{38} + 1244984q^{39} + 737000q^{40} - 333990q^{41} - 1649808q^{42} - 75908q^{43} + 1281936q^{44} - 508175q^{45} - 2114440q^{46} - 502344q^{47} + 1964032q^{48} + 2007993q^{49} + 963750q^{50} + 741160q^{51} - 1415784q^{52} - 3672078q^{53} - 2605760q^{54} - 1570700q^{55} + 835200q^{56} + 2021840q^{57} + 3386980q^{58} + 420420q^{59} + 2720800q^{60} + 4095110q^{61} + 4839072q^{62} - 1831968q^{63} - 9543232q^{64} - 5423350q^{65} - 1696480q^{66} + 3719156q^{67} - 5744952q^{68} - 3256176q^{69} + 2616600q^{70} + 4761960q^{71} + 1178760q^{72} + 301582q^{73} + 5924436q^{74} + 2172500q^{75} - 711600q^{76} + 2894832q^{77} + 7266064q^{78} + 2212560q^{79} - 7307600q^{80} - 9376595q^{81} - 12540308q^{82} - 3652188q^{83} + 5293536q^{84} + 10330550q^{85} + 2516160q^{86} - 20541640q^{87} + 10712160q^{88} + 19324530q^{89} + 2522150q^{90} - 20224640q^{91} - 6316944q^{92} + 14003664q^{93} + 11291656q^{94} - 7058500q^{95} + 2476160q^{96} - 272394q^{97} - 38814042q^{98} - 12697996q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.8.a \(\chi_{5}(1, \cdot)\) 5.8.a.a 1 1
5.8.a.b 2
5.8.b \(\chi_{5}(4, \cdot)\) 5.8.b.a 2 1