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Properties

Label 133.2
Level 133
Weight 2
Dimension 599
Nonzero newspaces 16
Newform subspaces 39
Sturm bound 2880
Trace bound 7

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Defining parameters

Level: \( N \) = \( 133 = 7 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 39 \)
Sturm bound: \(2880\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(133))\).

Total New Old
Modular forms 828 771 57
Cusp forms 613 599 14
Eisenstein series 215 172 43

Trace form

\( 599 q - 39 q^{2} - 40 q^{3} - 43 q^{4} - 42 q^{5} - 48 q^{6} - 46 q^{7} - 105 q^{8} - 49 q^{9} + O(q^{10}) \) \( 599 q - 39 q^{2} - 40 q^{3} - 43 q^{4} - 42 q^{5} - 48 q^{6} - 46 q^{7} - 105 q^{8} - 49 q^{9} - 54 q^{10} - 48 q^{11} - 40 q^{12} - 26 q^{13} - 30 q^{14} - 78 q^{15} + 5 q^{16} - 36 q^{17} - 3 q^{18} - 13 q^{19} - 42 q^{20} - 28 q^{21} - 72 q^{22} - 42 q^{23} - 24 q^{24} - 31 q^{25} - 42 q^{26} - 34 q^{27} - 13 q^{28} - 84 q^{29} + 18 q^{30} - 32 q^{31} - 9 q^{32} + 24 q^{33} - 15 q^{35} + 35 q^{36} - 20 q^{37} + 33 q^{38} - 20 q^{39} + 36 q^{40} - 42 q^{41} + 33 q^{42} - 56 q^{43} + 24 q^{44} + 48 q^{45} + 54 q^{46} + 6 q^{47} + 92 q^{48} - 28 q^{49} + 15 q^{50} - 2 q^{52} - 18 q^{53} + 6 q^{54} - 36 q^{55} + 57 q^{56} - 76 q^{57} - 90 q^{58} - 6 q^{59} + 102 q^{60} + 34 q^{61} + 66 q^{62} + 26 q^{63} + 59 q^{64} + 78 q^{65} + 108 q^{66} + 82 q^{67} + 90 q^{68} + 66 q^{69} + 81 q^{70} - 36 q^{71} + 165 q^{72} + 58 q^{73} + 30 q^{74} + 26 q^{75} + 11 q^{76} - 3 q^{77} + 30 q^{78} + 88 q^{79} + 102 q^{80} + 77 q^{81} + 180 q^{82} + 6 q^{83} + 143 q^{84} + 18 q^{85} + 30 q^{86} + 132 q^{87} + 108 q^{88} + 36 q^{89} + 144 q^{90} + 25 q^{91} - 24 q^{92} + 40 q^{93} + 54 q^{94} - 24 q^{95} + 108 q^{96} - 8 q^{97} + 123 q^{98} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)

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
133.2.a \(\chi_{133}(1, \cdot)\) 133.2.a.a 2 1
133.2.a.b 2
133.2.a.c 2
133.2.a.d 3
133.2.c \(\chi_{133}(132, \cdot)\) 133.2.c.a 2 1
133.2.c.b 4
133.2.c.c 4
133.2.e \(\chi_{133}(64, \cdot)\) 133.2.e.a 4 2
133.2.e.b 6
133.2.e.c 10
133.2.f \(\chi_{133}(39, \cdot)\) 133.2.f.a 2 2
133.2.f.b 4
133.2.f.c 4
133.2.f.d 14
133.2.g \(\chi_{133}(30, \cdot)\) 133.2.g.a 24 2
133.2.h \(\chi_{133}(11, \cdot)\) 133.2.h.a 24 2
133.2.i \(\chi_{133}(12, \cdot)\) 133.2.i.a 2 2
133.2.i.b 2
133.2.i.c 4
133.2.i.d 16
133.2.o \(\chi_{133}(75, \cdot)\) 133.2.o.a 4 2
133.2.o.b 4
133.2.o.c 4
133.2.o.d 6
133.2.o.e 6
133.2.p \(\chi_{133}(27, \cdot)\) 133.2.p.a 4 2
133.2.p.b 4
133.2.p.c 12
133.2.s \(\chi_{133}(31, \cdot)\) 133.2.s.a 2 2
133.2.s.b 2
133.2.s.c 4
133.2.s.d 16
133.2.u \(\chi_{133}(9, \cdot)\) 133.2.u.a 66 6
133.2.v \(\chi_{133}(36, \cdot)\) 133.2.v.a 30 6
133.2.v.b 30
133.2.w \(\chi_{133}(4, \cdot)\) 133.2.w.a 66 6
133.2.ba \(\chi_{133}(13, \cdot)\) 133.2.ba.a 72 6
133.2.bb \(\chi_{133}(3, \cdot)\) 133.2.bb.a 66 6
133.2.bf \(\chi_{133}(10, \cdot)\) 133.2.bf.a 66 6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(133))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(133)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 1}\)