Properties

Label 180.1
Level 180
Weight 1
Dimension 10
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 1728
Trace bound 4

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Defining parameters

Level: \( N \) = \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(1728\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(180))\).

Total New Old
Modular forms 170 36 134
Cusp forms 10 10 0
Eisenstein series 160 26 134

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10q - 4q^{4} - 2q^{5} + 4q^{6} - 2q^{9} + O(q^{10}) \) \( 10q - 4q^{4} - 2q^{5} + 4q^{6} - 2q^{9} - 2q^{10} - 4q^{13} + 2q^{14} - 4q^{16} - 2q^{20} - 4q^{21} - 2q^{24} - 4q^{25} + 2q^{29} - 2q^{30} + 4q^{34} + 4q^{36} - 4q^{37} + 6q^{40} + 2q^{41} + 4q^{45} - 4q^{46} - 2q^{49} + 4q^{52} - 2q^{54} + 2q^{56} + 4q^{58} - 2q^{61} + 2q^{64} + 2q^{69} + 2q^{70} + 4q^{73} + 4q^{80} - 2q^{81} - 4q^{82} + 2q^{84} + 4q^{85} - 4q^{86} - 4q^{89} + 2q^{94} - 2q^{96} + 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)

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
180.1.b \(\chi_{180}(89, \cdot)\) None 0 1
180.1.c \(\chi_{180}(91, \cdot)\) None 0 1
180.1.f \(\chi_{180}(19, \cdot)\) 180.1.f.a 2 1
180.1.g \(\chi_{180}(161, \cdot)\) None 0 1
180.1.l \(\chi_{180}(37, \cdot)\) None 0 2
180.1.m \(\chi_{180}(107, \cdot)\) 180.1.m.a 4 2
180.1.o \(\chi_{180}(41, \cdot)\) None 0 2
180.1.p \(\chi_{180}(79, \cdot)\) 180.1.p.a 2 2
180.1.p.b 2
180.1.s \(\chi_{180}(31, \cdot)\) None 0 2
180.1.t \(\chi_{180}(29, \cdot)\) None 0 2
180.1.u \(\chi_{180}(13, \cdot)\) None 0 4
180.1.v \(\chi_{180}(23, \cdot)\) None 0 4