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Properties

Label 39.3
Level 39
Weight 3
Dimension 72
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 336
Trace bound 4

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Defining parameters

Level: \( N \) = \( 39 = 3 \cdot 13 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(336\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(39))\).

Total New Old
Modular forms 136 92 44
Cusp forms 88 72 16
Eisenstein series 48 20 28

Trace form

\( 72 q - 6 q^{3} - 12 q^{4} - 6 q^{6} - 32 q^{7} - 72 q^{8} - 12 q^{9} + O(q^{10}) \) \( 72 q - 6 q^{3} - 12 q^{4} - 6 q^{6} - 32 q^{7} - 72 q^{8} - 12 q^{9} - 72 q^{10} - 12 q^{11} - 12 q^{12} + 12 q^{13} + 48 q^{14} + 30 q^{15} + 148 q^{16} + 12 q^{17} - 96 q^{18} - 44 q^{19} - 96 q^{20} - 84 q^{21} - 192 q^{22} - 48 q^{23} - 30 q^{24} - 24 q^{25} + 60 q^{26} + 60 q^{27} + 216 q^{28} + 120 q^{29} + 426 q^{30} + 132 q^{31} + 420 q^{32} + 276 q^{33} + 420 q^{34} + 240 q^{35} + 288 q^{36} + 60 q^{37} - 126 q^{39} - 552 q^{40} - 420 q^{41} - 420 q^{42} - 524 q^{43} - 420 q^{44} - 324 q^{45} - 612 q^{46} - 192 q^{47} - 606 q^{48} - 188 q^{49} - 192 q^{50} - 324 q^{51} - 408 q^{52} - 120 q^{53} - 342 q^{54} + 48 q^{55} - 36 q^{56} + 48 q^{57} + 336 q^{58} + 204 q^{59} + 396 q^{60} + 816 q^{61} + 516 q^{62} + 384 q^{63} + 912 q^{64} + 636 q^{65} + 1104 q^{66} + 388 q^{67} + 360 q^{68} + 492 q^{69} + 720 q^{70} + 168 q^{71} + 960 q^{72} + 244 q^{73} + 156 q^{74} + 180 q^{75} + 4 q^{76} + 96 q^{78} - 192 q^{79} - 288 q^{80} - 12 q^{81} - 672 q^{82} - 252 q^{83} - 1008 q^{84} - 696 q^{85} - 1008 q^{86} - 1170 q^{87} - 1200 q^{88} - 1056 q^{89} - 2040 q^{90} - 1112 q^{91} - 600 q^{92} - 1224 q^{93} - 396 q^{94} - 720 q^{95} - 288 q^{96} + 288 q^{97} - 156 q^{98} - 84 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)

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
39.3.c \(\chi_{39}(14, \cdot)\) 39.3.c.a 8 1
39.3.d \(\chi_{39}(38, \cdot)\) 39.3.d.a 2 1
39.3.d.b 2
39.3.d.c 4
39.3.g \(\chi_{39}(31, \cdot)\) 39.3.g.a 8 2
39.3.h \(\chi_{39}(17, \cdot)\) 39.3.h.a 2 2
39.3.h.b 12
39.3.i \(\chi_{39}(29, \cdot)\) 39.3.i.a 2 2
39.3.i.b 12
39.3.l \(\chi_{39}(7, \cdot)\) 39.3.l.a 8 4
39.3.l.b 12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(39))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(39)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)