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Properties

Label 132.2
Level 132
Weight 2
Dimension 190
Nonzero newspaces 8
Newform subspaces 15
Sturm bound 1920
Trace bound 1

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Defining parameters

Level: \( N \) = \( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 15 \)
Sturm bound: \(1920\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(132))\).

Total New Old
Modular forms 580 222 358
Cusp forms 381 190 191
Eisenstein series 199 32 167

Trace form

\( 190 q - 10 q^{4} - 5 q^{6} + 10 q^{7} + O(q^{10}) \) \( 190 q - 10 q^{4} - 5 q^{6} + 10 q^{7} - 20 q^{10} + 10 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 50 q^{16} - 10 q^{17} - 15 q^{18} - 30 q^{19} - 50 q^{20} - 40 q^{21} - 70 q^{22} - 20 q^{23} - 35 q^{24} - 60 q^{25} - 50 q^{26} - 15 q^{27} - 60 q^{28} - 20 q^{29} - 10 q^{30} - 20 q^{31} - 50 q^{33} + 20 q^{34} - 20 q^{35} + 35 q^{36} - 100 q^{37} + 50 q^{38} - 35 q^{39} + 60 q^{40} - 60 q^{41} + 60 q^{42} + 70 q^{44} - 95 q^{45} + 40 q^{46} + 10 q^{47} + 50 q^{48} - 30 q^{49} + 70 q^{50} + 5 q^{51} + 40 q^{52} - 50 q^{53} + 70 q^{54} + 20 q^{55} + 40 q^{56} + 35 q^{57} + 30 q^{59} + 90 q^{60} + 30 q^{61} + 65 q^{63} - 10 q^{64} + 60 q^{65} + 60 q^{66} + 50 q^{67} + 35 q^{69} + 60 q^{70} + 40 q^{71} + 80 q^{72} + 30 q^{73} + 50 q^{74} + 75 q^{75} + 60 q^{76} + 50 q^{77} + 100 q^{78} + 30 q^{79} + 110 q^{80} + 40 q^{81} + 90 q^{82} + 30 q^{83} + 70 q^{84} + 30 q^{85} + 80 q^{86} + 150 q^{88} + 40 q^{89} - 20 q^{90} - 50 q^{91} + 30 q^{92} - 30 q^{93} + 40 q^{94} - 30 q^{95} - 40 q^{96} - 80 q^{97} - 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)

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
132.2.a \(\chi_{132}(1, \cdot)\) 132.2.a.a 1 1
132.2.a.b 1
132.2.b \(\chi_{132}(65, \cdot)\) 132.2.b.a 4 1
132.2.c \(\chi_{132}(23, \cdot)\) 132.2.c.a 2 1
132.2.c.b 2
132.2.c.c 8
132.2.c.d 8
132.2.h \(\chi_{132}(43, \cdot)\) 132.2.h.a 12 1
132.2.i \(\chi_{132}(25, \cdot)\) 132.2.i.a 4 4
132.2.i.b 4
132.2.j \(\chi_{132}(7, \cdot)\) 132.2.j.a 48 4
132.2.o \(\chi_{132}(47, \cdot)\) 132.2.o.a 8 4
132.2.o.b 8
132.2.o.c 64
132.2.p \(\chi_{132}(17, \cdot)\) 132.2.p.a 16 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(132))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(132)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)