Properties

Label 68.3
Level 68
Weight 3
Dimension 152
Nonzero newspaces 5
Newform subspaces 11
Sturm bound 864
Trace bound 4

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Defining parameters

Level: \( N \) = \( 68 = 2^{2} \cdot 17 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 11 \)
Sturm bound: \(864\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(68))\).

Total New Old
Modular forms 328 180 148
Cusp forms 248 152 96
Eisenstein series 80 28 52

Trace form

\( 152 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + O(q^{10}) \) \( 152 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} + 40 q^{11} - 8 q^{12} + 8 q^{13} - 8 q^{14} + 24 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{18} - 24 q^{19} - 8 q^{20} - 136 q^{21} - 8 q^{22} - 56 q^{23} - 152 q^{24} - 248 q^{25} - 232 q^{26} - 144 q^{27} - 248 q^{28} - 96 q^{29} - 200 q^{30} - 64 q^{31} - 48 q^{32} - 32 q^{33} + 56 q^{34} + 64 q^{35} + 184 q^{36} + 112 q^{37} + 192 q^{38} + 368 q^{39} + 440 q^{40} + 360 q^{41} + 424 q^{42} + 352 q^{43} + 344 q^{44} + 384 q^{45} + 200 q^{46} + 120 q^{47} + 64 q^{48} + 16 q^{49} - 16 q^{50} - 32 q^{51} - 16 q^{52} - 280 q^{53} + 584 q^{54} - 352 q^{55} + 432 q^{56} - 1176 q^{57} + 496 q^{58} - 416 q^{59} + 720 q^{60} - 480 q^{61} + 272 q^{62} - 504 q^{63} + 136 q^{64} - 472 q^{65} + 64 q^{66} - 96 q^{68} + 400 q^{69} - 240 q^{70} + 272 q^{71} - 528 q^{72} + 1072 q^{73} - 344 q^{74} + 672 q^{75} - 512 q^{76} + 688 q^{77} - 1152 q^{78} + 352 q^{79} - 936 q^{80} + 1360 q^{81} - 608 q^{82} + 136 q^{83} - 1376 q^{84} - 360 q^{85} - 1216 q^{86} - 816 q^{87} - 840 q^{88} - 712 q^{89} - 1528 q^{90} - 976 q^{91} - 1016 q^{92} - 816 q^{93} - 680 q^{94} - 832 q^{95} - 768 q^{96} - 560 q^{97} - 416 q^{98} - 440 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(68))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
68.3.c \(\chi_{68}(35, \cdot)\) 68.3.c.a 16 1
68.3.d \(\chi_{68}(67, \cdot)\) 68.3.d.a 2 1
68.3.d.b 2
68.3.d.c 12
68.3.f \(\chi_{68}(47, \cdot)\) 68.3.f.a 32 2
68.3.g \(\chi_{68}(15, \cdot)\) 68.3.g.a 4 4
68.3.g.b 4
68.3.g.c 4
68.3.g.d 4
68.3.g.e 48
68.3.j \(\chi_{68}(5, \cdot)\) 68.3.j.a 24 8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(68))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(68)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)