Properties

Label 10.6
Level 10
Weight 6
Dimension 5
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 36
Trace bound 1

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(36\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(10))\).

Total New Old
Modular forms 19 5 14
Cusp forms 11 5 6
Eisenstein series 8 0 8

Trace form

\( 5 q - 4 q^{2} + 4 q^{3} + 16 q^{4} + 85 q^{5} - 80 q^{6} - 312 q^{7} - 64 q^{8} + 653 q^{9} + O(q^{10}) \) \( 5 q - 4 q^{2} + 4 q^{3} + 16 q^{4} + 85 q^{5} - 80 q^{6} - 312 q^{7} - 64 q^{8} + 653 q^{9} - 180 q^{10} - 740 q^{11} + 64 q^{12} + 114 q^{13} + 1568 q^{14} + 820 q^{15} + 1280 q^{16} + 918 q^{17} - 3892 q^{18} - 5580 q^{19} - 2160 q^{20} + 160 q^{21} + 3312 q^{22} + 3144 q^{23} + 2304 q^{24} + 7725 q^{25} + 2920 q^{26} - 5480 q^{27} - 4992 q^{28} + 3030 q^{29} - 11760 q^{30} - 12640 q^{31} - 1024 q^{32} + 24288 q^{33} + 18808 q^{34} + 2360 q^{35} + 7440 q^{36} - 16902 q^{37} - 17360 q^{38} - 34024 q^{39} - 320 q^{40} - 2390 q^{41} + 11392 q^{42} + 13164 q^{43} - 2368 q^{44} + 7845 q^{45} + 9920 q^{46} + 44448 q^{47} + 1024 q^{48} - 22743 q^{49} - 11300 q^{50} + 46760 q^{51} + 1824 q^{52} - 44406 q^{53} - 32160 q^{54} + 1420 q^{55} - 15360 q^{56} - 33040 q^{57} + 37320 q^{58} + 80860 q^{59} + 22080 q^{60} - 72290 q^{61} - 20768 q^{62} - 42376 q^{63} + 4096 q^{64} - 63830 q^{65} - 71360 q^{66} + 10788 q^{67} + 14688 q^{68} + 181456 q^{69} + 96320 q^{70} + 79560 q^{71} - 62272 q^{72} - 9666 q^{73} - 11512 q^{74} - 28300 q^{75} + 52800 q^{76} - 28464 q^{77} + 112576 q^{78} - 151920 q^{79} + 21760 q^{80} - 62595 q^{81} - 12648 q^{82} - 220476 q^{83} - 139008 q^{84} + 6910 q^{85} - 90480 q^{86} + 233880 q^{87} + 52992 q^{88} + 156290 q^{89} + 26940 q^{90} + 249360 q^{91} + 50304 q^{92} + 117968 q^{93} - 158272 q^{94} - 190700 q^{95} - 20480 q^{96} - 224682 q^{97} + 2652 q^{98} - 342244 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.6.a \(\chi_{10}(1, \cdot)\) 10.6.a.a 1 1
10.6.a.b 1
10.6.a.c 1
10.6.b \(\chi_{10}(9, \cdot)\) 10.6.b.a 2 1

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)