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Properties

Label 69.4
Level 69
Weight 4
Dimension 374
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 1408
Trace bound 1

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Defining parameters

Level: \( N \) = \( 69 = 3 \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(1408\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(69))\).

Total New Old
Modular forms 572 418 154
Cusp forms 484 374 110
Eisenstein series 88 44 44

Trace form

\( 374 q - 11 q^{3} - 22 q^{4} - 11 q^{6} - 22 q^{7} - 11 q^{9} + O(q^{10}) \) \( 374 q - 11 q^{3} - 22 q^{4} - 11 q^{6} - 22 q^{7} - 11 q^{9} - 22 q^{10} - 11 q^{12} - 22 q^{13} + 363 q^{15} + 858 q^{16} + 176 q^{17} - 99 q^{18} - 242 q^{19} - 1408 q^{20} - 671 q^{21} - 968 q^{22} - 968 q^{23} - 1342 q^{24} - 726 q^{25} - 440 q^{26} - 77 q^{27} + 682 q^{28} + 440 q^{29} + 1485 q^{30} + 1078 q^{31} + 2992 q^{32} + 957 q^{33} + 3806 q^{34} + 2860 q^{35} + 979 q^{36} + 2354 q^{37} + 1210 q^{38} - 143 q^{39} - 2662 q^{40} - 1100 q^{41} - 3641 q^{42} - 3454 q^{43} - 6622 q^{44} - 7942 q^{46} - 3784 q^{47} - 3355 q^{48} - 4378 q^{49} - 3850 q^{50} - 671 q^{51} - 682 q^{52} + 484 q^{53} - 2541 q^{54} + 3938 q^{55} + 7150 q^{56} + 1705 q^{57} + 12188 q^{58} + 6028 q^{59} + 3179 q^{60} - 22 q^{61} + 2079 q^{63} - 22 q^{64} + 5742 q^{66} - 22 q^{67} + 3729 q^{69} - 44 q^{70} + 7381 q^{72} - 22 q^{73} + 4730 q^{74} + 9955 q^{75} + 16368 q^{76} + 10472 q^{77} + 8547 q^{78} + 5698 q^{79} + 8118 q^{80} - 1375 q^{81} - 154 q^{82} - 1672 q^{83} - 16753 q^{84} - 10802 q^{85} - 13420 q^{86} - 9383 q^{87} - 12518 q^{88} - 11220 q^{89} - 18700 q^{90} - 16016 q^{91} - 18018 q^{92} - 11770 q^{93} - 16676 q^{94} - 8052 q^{95} - 5522 q^{96} + 4598 q^{97} + 5280 q^{98} - 1859 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
69.4.a \(\chi_{69}(1, \cdot)\) 69.4.a.a 2 1
69.4.a.b 2
69.4.a.c 4
69.4.a.d 4
69.4.c \(\chi_{69}(68, \cdot)\) 69.4.c.a 2 1
69.4.c.b 4
69.4.c.c 16
69.4.e \(\chi_{69}(4, \cdot)\) 69.4.e.a 60 10
69.4.e.b 60
69.4.g \(\chi_{69}(5, \cdot)\) 69.4.g.a 220 10

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(69))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(69)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)