Properties

Label 15.8
Level 15
Weight 8
Dimension 36
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 128
Trace bound 1

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(128\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(15))\).

Total New Old
Modular forms 64 44 20
Cusp forms 48 36 12
Eisenstein series 16 8 8

Trace form

\( 36 q - 28 q^{2} + 78 q^{3} - 200 q^{4} - 444 q^{5} + 1356 q^{6} + 3608 q^{7} - 2436 q^{8} - 2916 q^{9} + O(q^{10}) \) \( 36 q - 28 q^{2} + 78 q^{3} - 200 q^{4} - 444 q^{5} + 1356 q^{6} + 3608 q^{7} - 2436 q^{8} - 2916 q^{9} - 4616 q^{10} + 7952 q^{11} + 8340 q^{12} + 5360 q^{13} - 34488 q^{14} + 26814 q^{15} + 38000 q^{16} - 32032 q^{17} - 126972 q^{18} - 64176 q^{19} + 46444 q^{20} + 134904 q^{21} + 146376 q^{22} + 170088 q^{23} - 237168 q^{24} - 85644 q^{25} - 445816 q^{26} - 224802 q^{27} + 436280 q^{28} + 717688 q^{29} + 774336 q^{30} + 71568 q^{31} - 1063916 q^{32} - 774984 q^{33} + 238760 q^{34} + 636520 q^{35} + 569016 q^{36} - 789232 q^{37} - 769432 q^{38} - 1224396 q^{39} - 2054392 q^{40} + 883240 q^{41} + 1622112 q^{42} + 976328 q^{43} + 537976 q^{44} + 893916 q^{45} + 4371848 q^{46} + 1210520 q^{47} + 1149684 q^{48} - 2687956 q^{49} - 5555236 q^{50} - 4088820 q^{51} - 8572528 q^{52} + 1575488 q^{53} - 393660 q^{54} + 7062576 q^{55} + 6479040 q^{56} + 5320296 q^{57} - 1200264 q^{58} - 1197184 q^{59} + 6515256 q^{60} + 1179144 q^{61} + 5573928 q^{62} - 323496 q^{63} + 9724488 q^{64} - 3366592 q^{65} - 30638208 q^{66} - 21756808 q^{67} - 9434504 q^{68} - 5890968 q^{69} - 1513560 q^{70} - 4007216 q^{71} + 34470036 q^{72} + 6676736 q^{73} + 20919712 q^{74} + 19838094 q^{75} + 37710128 q^{76} + 6733248 q^{77} - 10796952 q^{78} - 10874880 q^{79} - 39917876 q^{80} - 24912684 q^{81} - 40630392 q^{82} - 17321256 q^{83} - 43954272 q^{84} - 33002768 q^{85} - 6212848 q^{86} + 50204484 q^{87} + 97866504 q^{88} + 58210824 q^{89} + 80324424 q^{90} + 88309648 q^{91} + 15479424 q^{92} - 54464928 q^{93} - 78524776 q^{94} - 33956656 q^{95} - 104433168 q^{96} - 63625168 q^{97} - 21248492 q^{98} - 9879408 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.8.a \(\chi_{15}(1, \cdot)\) 15.8.a.a 1 1
15.8.a.b 1
15.8.a.c 2
15.8.b \(\chi_{15}(4, \cdot)\) 15.8.b.a 8 1
15.8.e \(\chi_{15}(2, \cdot)\) 15.8.e.a 24 2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)