↑

Properties

Label 3.8
Level 3
Weight 8
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 5
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(3))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

Trace form

\( q + 6 q^{2} - 27 q^{3} - 92 q^{4} + 390 q^{5} - 162 q^{6} - 64 q^{7} - 1320 q^{8} + 729 q^{9} + O(q^{10}) \) \( q + 6 q^{2} - 27 q^{3} - 92 q^{4} + 390 q^{5} - 162 q^{6} - 64 q^{7} - 1320 q^{8} + 729 q^{9} + 2340 q^{10} - 948 q^{11} + 2484 q^{12} - 5098 q^{13} - 384 q^{14} - 10530 q^{15} + 3856 q^{16} + 28386 q^{17} + 4374 q^{18} - 8620 q^{19} - 35880 q^{20} + 1728 q^{21} - 5688 q^{22} - 15288 q^{23} + 35640 q^{24} + 73975 q^{25} - 30588 q^{26} - 19683 q^{27} + 5888 q^{28} + 36510 q^{29} - 63180 q^{30} - 276808 q^{31} + 192096 q^{32} + 25596 q^{33} + 170316 q^{34} - 24960 q^{35} - 67068 q^{36} + 268526 q^{37} - 51720 q^{38} + 137646 q^{39} - 514800 q^{40} - 629718 q^{41} + 10368 q^{42} + 685772 q^{43} + 87216 q^{44} + 284310 q^{45} - 91728 q^{46} + 583296 q^{47} - 104112 q^{48} - 819447 q^{49} + 443850 q^{50} - 766422 q^{51} + 469016 q^{52} - 428058 q^{53} - 118098 q^{54} - 369720 q^{55} + 84480 q^{56} + 232740 q^{57} + 219060 q^{58} + 1306380 q^{59} + 968760 q^{60} + 300662 q^{61} - 1660848 q^{62} - 46656 q^{63} + 659008 q^{64} - 1988220 q^{65} + 153576 q^{66} - 507244 q^{67} - 2611512 q^{68} + 412776 q^{69} - 149760 q^{70} + 5560632 q^{71} - 962280 q^{72} + 1369082 q^{73} + 1611156 q^{74} - 1997325 q^{75} + 793040 q^{76} + 60672 q^{77} + 825876 q^{78} - 6913720 q^{79} + 1503840 q^{80} + 531441 q^{81} - 3778308 q^{82} - 4376748 q^{83} - 158976 q^{84} + 11070540 q^{85} + 4114632 q^{86} - 985770 q^{87} + 1251360 q^{88} - 8528310 q^{89} + 1705860 q^{90} + 326272 q^{91} + 1406496 q^{92} + 7473816 q^{93} + 3499776 q^{94} - 3361800 q^{95} - 5186592 q^{96} - 8826814 q^{97} - 4916682 q^{98} - 691092 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.8.a \(\chi_{3}(1, \cdot)\) 3.8.a.a 1 1