Properties

Label 5.6
Level 5
Weight 6
Dimension 3
Nonzero newspaces 2
Newforms 2
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(5))\).

Total New Old
Modular forms 7 5 2
Cusp forms 3 3 0
Eisenstein series 4 2 2

Trace form

\(3q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 52q^{4} \) \(\mathstrut -\mathstrut 65q^{5} \) \(\mathstrut +\mathstrut 256q^{6} \) \(\mathstrut +\mathstrut 192q^{7} \) \(\mathstrut -\mathstrut 120q^{8} \) \(\mathstrut -\mathstrut 533q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 52q^{4} \) \(\mathstrut -\mathstrut 65q^{5} \) \(\mathstrut +\mathstrut 256q^{6} \) \(\mathstrut +\mathstrut 192q^{7} \) \(\mathstrut -\mathstrut 120q^{8} \) \(\mathstrut -\mathstrut 533q^{9} \) \(\mathstrut -\mathstrut 390q^{10} \) \(\mathstrut +\mathstrut 356q^{11} \) \(\mathstrut +\mathstrut 112q^{12} \) \(\mathstrut +\mathstrut 286q^{13} \) \(\mathstrut +\mathstrut 1176q^{14} \) \(\mathstrut +\mathstrut 1220q^{15} \) \(\mathstrut -\mathstrut 1872q^{16} \) \(\mathstrut -\mathstrut 1678q^{17} \) \(\mathstrut -\mathstrut 454q^{18} \) \(\mathstrut +\mathstrut 620q^{19} \) \(\mathstrut +\mathstrut 380q^{20} \) \(\mathstrut -\mathstrut 3144q^{21} \) \(\mathstrut -\mathstrut 296q^{22} \) \(\mathstrut +\mathstrut 2976q^{23} \) \(\mathstrut +\mathstrut 5760q^{24} \) \(\mathstrut +\mathstrut 2475q^{25} \) \(\mathstrut +\mathstrut 2156q^{26} \) \(\mathstrut +\mathstrut 1880q^{27} \) \(\mathstrut -\mathstrut 5376q^{28} \) \(\mathstrut -\mathstrut 17270q^{29} \) \(\mathstrut -\mathstrut 12080q^{30} \) \(\mathstrut +\mathstrut 11056q^{31} \) \(\mathstrut +\mathstrut 5152q^{32} \) \(\mathstrut +\mathstrut 592q^{33} \) \(\mathstrut +\mathstrut 5796q^{34} \) \(\mathstrut +\mathstrut 8760q^{35} \) \(\mathstrut +\mathstrut 10028q^{36} \) \(\mathstrut +\mathstrut 182q^{37} \) \(\mathstrut +\mathstrut 2120q^{38} \) \(\mathstrut -\mathstrut 5896q^{39} \) \(\mathstrut -\mathstrut 11800q^{40} \) \(\mathstrut -\mathstrut 9794q^{41} \) \(\mathstrut -\mathstrut 1536q^{42} \) \(\mathstrut -\mathstrut 1244q^{43} \) \(\mathstrut -\mathstrut 1904q^{44} \) \(\mathstrut +\mathstrut 8095q^{45} \) \(\mathstrut -\mathstrut 26344q^{46} \) \(\mathstrut -\mathstrut 12088q^{47} \) \(\mathstrut -\mathstrut 2624q^{48} \) \(\mathstrut +\mathstrut 46543q^{49} \) \(\mathstrut +\mathstrut 40850q^{50} \) \(\mathstrut -\mathstrut 20744q^{51} \) \(\mathstrut -\mathstrut 8008q^{52} \) \(\mathstrut +\mathstrut 23846q^{53} \) \(\mathstrut +\mathstrut 27520q^{54} \) \(\mathstrut -\mathstrut 26380q^{55} \) \(\mathstrut -\mathstrut 7200q^{56} \) \(\mathstrut -\mathstrut 4240q^{57} \) \(\mathstrut -\mathstrut 6820q^{58} \) \(\mathstrut -\mathstrut 69340q^{59} \) \(\mathstrut -\mathstrut 13040q^{60} \) \(\mathstrut +\mathstrut 20906q^{61} \) \(\mathstrut -\mathstrut 4896q^{62} \) \(\mathstrut -\mathstrut 43584q^{63} \) \(\mathstrut -\mathstrut 36672q^{64} \) \(\mathstrut +\mathstrut 15070q^{65} \) \(\mathstrut +\mathstrut 67712q^{66} \) \(\mathstrut +\mathstrut 60972q^{67} \) \(\mathstrut +\mathstrut 46984q^{68} \) \(\mathstrut +\mathstrut 84984q^{69} \) \(\mathstrut -\mathstrut 26040q^{70} \) \(\mathstrut +\mathstrut 74056q^{71} \) \(\mathstrut +\mathstrut 27240q^{72} \) \(\mathstrut -\mathstrut 38774q^{73} \) \(\mathstrut -\mathstrut 184964q^{74} \) \(\mathstrut -\mathstrut 121300q^{75} \) \(\mathstrut -\mathstrut 24400q^{76} \) \(\mathstrut -\mathstrut 28416q^{77} \) \(\mathstrut -\mathstrut 2288q^{78} \) \(\mathstrut +\mathstrut 70480q^{79} \) \(\mathstrut +\mathstrut 130160q^{80} \) \(\mathstrut -\mathstrut 97997q^{81} \) \(\mathstrut -\mathstrut 18796q^{82} \) \(\mathstrut +\mathstrut 16716q^{83} \) \(\mathstrut +\mathstrut 50016q^{84} \) \(\mathstrut +\mathstrut 3810q^{85} \) \(\mathstrut +\mathstrut 3056q^{86} \) \(\mathstrut +\mathstrut 13640q^{87} \) \(\mathstrut +\mathstrut 17760q^{88} \) \(\mathstrut +\mathstrut 81390q^{89} \) \(\mathstrut +\mathstrut 55970q^{90} \) \(\mathstrut +\mathstrut 40656q^{91} \) \(\mathstrut -\mathstrut 83328q^{92} \) \(\mathstrut +\mathstrut 9792q^{93} \) \(\mathstrut +\mathstrut 115656q^{94} \) \(\mathstrut +\mathstrut 46300q^{95} \) \(\mathstrut -\mathstrut 185344q^{96} \) \(\mathstrut -\mathstrut 119038q^{97} \) \(\mathstrut +\mathstrut 40114q^{98} \) \(\mathstrut -\mathstrut 43516q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.6.a \(\chi_{5}(1, \cdot)\) 5.6.a.a 1 1
5.6.b \(\chi_{5}(4, \cdot)\) 5.6.b.a 2 1