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Properties

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

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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