Properties

Label 171.1
Level 171
Weight 1
Dimension 7
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 2160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(2160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(171))\).

Total New Old
Modular forms 155 84 71
Cusp forms 11 7 4
Eisenstein series 144 77 67

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 4 0 0

Trace form

\( 7q - 2q^{5} - 2q^{6} - 2q^{7} - 4q^{9} + O(q^{10}) \) \( 7q - 2q^{5} - 2q^{6} - 2q^{7} - 4q^{9} + 2q^{11} - 3q^{13} + 2q^{16} - 3q^{19} + 2q^{23} + 4q^{24} - 4q^{26} - 3q^{28} + 4q^{30} + 4q^{35} - 2q^{38} - 2q^{39} - 2q^{42} + q^{43} + 2q^{45} - 2q^{47} + 3q^{49} + 3q^{52} + 2q^{54} - 4q^{55} - 4q^{57} - 2q^{58} - q^{61} + 4q^{62} + 2q^{63} - q^{64} + 2q^{66} + 3q^{67} + 3q^{73} + 2q^{77} - 3q^{79} - 4q^{80} + 4q^{81} - 4q^{82} + 2q^{83} + 2q^{87} - 3q^{91} + 2q^{93} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(171))\)

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
171.1.b \(\chi_{171}(134, \cdot)\) None 0 1
171.1.c \(\chi_{171}(37, \cdot)\) 171.1.c.a 1 1
171.1.i \(\chi_{171}(88, \cdot)\) None 0 2
171.1.j \(\chi_{171}(68, \cdot)\) None 0 2
171.1.n \(\chi_{171}(11, \cdot)\) None 0 2
171.1.o \(\chi_{171}(94, \cdot)\) 171.1.o.a 4 2
171.1.p \(\chi_{171}(46, \cdot)\) 171.1.p.a 2 2
171.1.q \(\chi_{171}(20, \cdot)\) None 0 2
171.1.r \(\chi_{171}(26, \cdot)\) None 0 2
171.1.s \(\chi_{171}(31, \cdot)\) None 0 2
171.1.z \(\chi_{171}(5, \cdot)\) None 0 6
171.1.ba \(\chi_{171}(10, \cdot)\) None 0 6
171.1.bb \(\chi_{171}(17, \cdot)\) None 0 6
171.1.bc \(\chi_{171}(22, \cdot)\) None 0 6
171.1.be \(\chi_{171}(13, \cdot)\) None 0 6
171.1.bf \(\chi_{171}(23, \cdot)\) None 0 6

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(171))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(171)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)