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Properties

Label 69.3
Level 69
Weight 3
Dimension 242
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 1056
Trace bound 1

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Defining parameters

Level: \( N \) = \( 69 = 3 \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(1056\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(69))\).

Total New Old
Modular forms 396 282 114
Cusp forms 308 242 66
Eisenstein series 88 40 48

Trace form

\( 242 q - 11 q^{3} - 22 q^{4} - 11 q^{6} - 22 q^{7} - 11 q^{9} + O(q^{10}) \) \( 242 q - 11 q^{3} - 22 q^{4} - 11 q^{6} - 22 q^{7} - 11 q^{9} - 22 q^{10} - 11 q^{12} - 22 q^{13} - 88 q^{15} - 286 q^{16} - 110 q^{17} - 187 q^{18} - 88 q^{19} - 176 q^{20} - 44 q^{21} - 44 q^{22} + 44 q^{23} + 110 q^{24} + 110 q^{25} + 176 q^{26} + 154 q^{27} + 506 q^{28} + 154 q^{29} + 341 q^{30} + 176 q^{31} + 440 q^{32} + 110 q^{33} - 506 q^{34} - 440 q^{35} - 209 q^{36} - 726 q^{37} - 770 q^{38} - 275 q^{39} - 902 q^{40} - 176 q^{41} - 341 q^{42} - 198 q^{43} - 154 q^{44} - 22 q^{45} + 154 q^{46} + 176 q^{47} + 297 q^{48} + 506 q^{49} + 770 q^{50} + 253 q^{51} + 1518 q^{52} + 352 q^{53} + 495 q^{54} + 858 q^{55} + 1210 q^{56} + 880 q^{57} + 1408 q^{58} + 616 q^{59} + 1199 q^{60} - 22 q^{61} + 264 q^{63} - 22 q^{64} + 66 q^{66} - 22 q^{67} - 66 q^{69} - 44 q^{70} - 539 q^{72} - 22 q^{73} - 374 q^{74} - 1254 q^{75} - 1672 q^{76} - 1232 q^{77} - 2101 q^{78} - 1078 q^{79} - 2178 q^{80} - 1903 q^{81} - 1210 q^{82} - 704 q^{83} - 2145 q^{84} - 1342 q^{85} - 1100 q^{86} - 539 q^{87} - 902 q^{88} - 264 q^{89} - 176 q^{90} - 44 q^{91} + 198 q^{92} + 242 q^{93} + 660 q^{94} + 286 q^{95} + 66 q^{96} - 352 q^{97} - 176 q^{98} + 715 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(69))\)

We only show spaces with odd 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
69.3.b \(\chi_{69}(47, \cdot)\) 69.3.b.a 14 1
69.3.d \(\chi_{69}(22, \cdot)\) 69.3.d.a 8 1
69.3.f \(\chi_{69}(7, \cdot)\) 69.3.f.a 80 10
69.3.h \(\chi_{69}(2, \cdot)\) 69.3.h.a 140 10

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(69))\) into lower level spaces

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