Properties

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

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
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

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

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