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Properties

Label 129.3
Level 129
Weight 3
Dimension 882
Nonzero newspaces 8
Newform subspaces 13
Sturm bound 3696
Trace bound 1

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Defining parameters

Level: \( N \) = \( 129 = 3 \cdot 43 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 13 \)
Sturm bound: \(3696\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(129))\).

Total New Old
Modular forms 1316 962 354
Cusp forms 1148 882 266
Eisenstein series 168 80 88

Trace form

\( 882 q - 21 q^{3} - 42 q^{4} - 21 q^{6} - 42 q^{7} - 21 q^{9} + O(q^{10}) \) \( 882 q - 21 q^{3} - 42 q^{4} - 21 q^{6} - 42 q^{7} - 21 q^{9} - 42 q^{10} - 21 q^{12} - 42 q^{13} - 21 q^{15} - 42 q^{16} - 21 q^{18} - 42 q^{19} - 21 q^{21} - 42 q^{22} - 21 q^{24} - 42 q^{25} - 21 q^{27} - 42 q^{28} - 21 q^{30} - 196 q^{31} - 840 q^{32} - 399 q^{33} - 1050 q^{34} - 588 q^{35} - 189 q^{36} - 462 q^{37} - 672 q^{38} - 168 q^{39} - 714 q^{40} - 42 q^{41} - 42 q^{42} + 168 q^{43} + 336 q^{44} + 105 q^{45} + 630 q^{46} + 210 q^{47} + 987 q^{48} + 644 q^{49} + 1344 q^{50} + 357 q^{51} + 2198 q^{52} + 924 q^{53} - 21 q^{54} + 1050 q^{55} + 1176 q^{56} + 84 q^{57} - 42 q^{58} - 21 q^{60} - 42 q^{61} - 21 q^{63} - 42 q^{64} - 21 q^{66} - 42 q^{67} - 693 q^{69} - 2562 q^{70} - 1176 q^{71} - 2751 q^{72} - 1050 q^{73} - 3234 q^{74} - 1491 q^{75} - 2688 q^{76} - 2016 q^{77} - 1932 q^{78} - 1050 q^{79} - 1680 q^{80} - 693 q^{81} - 1302 q^{82} - 336 q^{83} - 315 q^{84} - 84 q^{85} + 336 q^{86} + 378 q^{87} + 1134 q^{88} + 672 q^{89} + 1869 q^{90} + 966 q^{91} + 2940 q^{92} + 1323 q^{93} + 2982 q^{94} + 1680 q^{95} + 2982 q^{96} + 2982 q^{97} + 3822 q^{98} + 2037 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(129))\)

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
129.3.b \(\chi_{129}(85, \cdot)\) 129.3.b.a 14 1
129.3.c \(\chi_{129}(44, \cdot)\) 129.3.c.a 28 1
129.3.f \(\chi_{129}(92, \cdot)\) 129.3.f.a 2 2
129.3.f.b 52
129.3.g \(\chi_{129}(7, \cdot)\) 129.3.g.a 2 2
129.3.g.b 14
129.3.g.c 14
129.3.k \(\chi_{129}(22, \cdot)\) 129.3.k.a 84 6
129.3.l \(\chi_{129}(11, \cdot)\) 129.3.l.a 168 6
129.3.o \(\chi_{129}(14, \cdot)\) 129.3.o.a 12 12
129.3.o.b 312
129.3.p \(\chi_{129}(19, \cdot)\) 129.3.p.a 84 12
129.3.p.b 96

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(129))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(129)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 2}\)