Properties

Label 189.1
Level 189
Weight 1
Dimension 4
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 2592
Trace bound 4

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Defining parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(2592\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(189))\).

Total New Old
Modular forms 186 84 102
Cusp forms 6 4 2
Eisenstein series 180 80 100

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

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

Trace form

\( 4q + O(q^{10}) \) \( 4q - 2q^{13} - 2q^{16} - 2q^{19} - 2q^{25} - 2q^{28} - 2q^{31} + 4q^{49} + 4q^{52} + 4q^{61} + 2q^{67} - 2q^{73} + 4q^{76} + 2q^{79} - 2q^{91} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(189))\)

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
189.1.b \(\chi_{189}(134, \cdot)\) None 0 1
189.1.d \(\chi_{189}(55, \cdot)\) None 0 1
189.1.j \(\chi_{189}(44, \cdot)\) None 0 2
189.1.k \(\chi_{189}(10, \cdot)\) None 0 2
189.1.l \(\chi_{189}(118, \cdot)\) None 0 2
189.1.m \(\chi_{189}(82, \cdot)\) 189.1.m.a 2 2
189.1.n \(\chi_{189}(170, \cdot)\) None 0 2
189.1.q \(\chi_{189}(53, \cdot)\) 189.1.q.a 2 2
189.1.r \(\chi_{189}(8, \cdot)\) None 0 2
189.1.t \(\chi_{189}(73, \cdot)\) None 0 2
189.1.x \(\chi_{189}(40, \cdot)\) None 0 6
189.1.y \(\chi_{189}(13, \cdot)\) None 0 6
189.1.z \(\chi_{189}(31, \cdot)\) None 0 6
189.1.bb \(\chi_{189}(29, \cdot)\) None 0 6
189.1.bc \(\chi_{189}(2, \cdot)\) None 0 6
189.1.bf \(\chi_{189}(11, \cdot)\) None 0 6

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(189))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(189)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)