Properties

Label 69.6
Level 69
Weight 6
Dimension 636
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 2112
Trace bound 1

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Defining parameters

Level: \( N \) = \( 69 = 3 \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(2112\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(69))\).

Total New Old
Modular forms 924 680 244
Cusp forms 836 636 200
Eisenstein series 88 44 44

Trace form

\( 636 q + 12 q^{2} - 29 q^{3} - 30 q^{4} - 12 q^{5} + 97 q^{6} + 58 q^{7} - 336 q^{8} - 173 q^{9} + O(q^{10}) \) \( 636 q + 12 q^{2} - 29 q^{3} - 30 q^{4} - 12 q^{5} + 97 q^{6} + 58 q^{7} - 336 q^{8} - 173 q^{9} + 50 q^{10} + 1128 q^{11} - 83 q^{12} - 1298 q^{13} - 480 q^{14} + 4512 q^{15} - 5494 q^{16} - 9706 q^{17} - 11535 q^{18} - 472 q^{19} + 15440 q^{20} + 13216 q^{21} + 14528 q^{22} + 21124 q^{23} + 17018 q^{24} + 7520 q^{25} - 6248 q^{26} - 23612 q^{27} - 82774 q^{28} - 31738 q^{29} - 32979 q^{30} - 9064 q^{31} + 59776 q^{32} + 51402 q^{33} + 162582 q^{34} + 32380 q^{35} - 20261 q^{36} - 139434 q^{37} - 198182 q^{38} - 72875 q^{39} - 138438 q^{40} + 12376 q^{41} + 73879 q^{42} + 99402 q^{43} + 282482 q^{44} - 972 q^{45} + 343242 q^{46} + 183512 q^{47} + 116621 q^{48} + 70652 q^{49} - 133318 q^{50} - 86771 q^{51} - 563706 q^{52} - 211424 q^{53} - 282213 q^{54} - 299054 q^{55} - 267170 q^{56} + 74314 q^{57} + 332724 q^{58} + 353188 q^{59} + 722147 q^{60} - 79538 q^{61} + 52800 q^{62} + 13674 q^{63} - 55446 q^{64} - 7656 q^{65} - 373290 q^{66} + 46114 q^{67} - 7056 q^{68} - 242976 q^{69} - 2924 q^{70} + 8496 q^{71} - 289115 q^{72} + 82198 q^{73} + 517538 q^{74} + 883198 q^{75} + 565536 q^{76} - 127048 q^{77} + 12639 q^{78} - 673150 q^{79} - 1570170 q^{80} - 773101 q^{81} - 959074 q^{82} - 600592 q^{83} - 975625 q^{84} - 155586 q^{85} + 461348 q^{86} + 398173 q^{87} + 1171034 q^{88} + 1094880 q^{89} + 1642148 q^{90} + 1508496 q^{91} + 1624782 q^{92} + 917246 q^{93} + 1039660 q^{94} + 1639710 q^{95} + 1433494 q^{96} + 514168 q^{97} - 615972 q^{98} - 724073 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(69))\)

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
69.6.a \(\chi_{69}(1, \cdot)\) 69.6.a.a 2 1
69.6.a.b 3
69.6.a.c 4
69.6.a.d 4
69.6.a.e 5
69.6.c \(\chi_{69}(68, \cdot)\) 69.6.c.a 6 1
69.6.c.b 32
69.6.e \(\chi_{69}(4, \cdot)\) 69.6.e.a 100 10
69.6.e.b 100
69.6.g \(\chi_{69}(5, \cdot)\) 69.6.g.a 380 10

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(69))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(69)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)