Properties

Label 225.1
Level 225
Weight 1
Dimension 2
Nonzero newspaces 1
Newforms 1
Sturm bound 3600
Trace bound 0

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Defining parameters

Level: \( N \) = \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(3600\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(225))\).

Total New Old
Modular forms 226 94 132
Cusp forms 2 2 0
Eisenstein series 224 92 132

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\(2q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)

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
225.1.c \(\chi_{225}(26, \cdot)\) None 0 1
225.1.d \(\chi_{225}(224, \cdot)\) None 0 1
225.1.g \(\chi_{225}(82, \cdot)\) 225.1.g.a 2 2
225.1.i \(\chi_{225}(74, \cdot)\) None 0 2
225.1.j \(\chi_{225}(101, \cdot)\) None 0 2
225.1.l \(\chi_{225}(44, \cdot)\) None 0 4
225.1.n \(\chi_{225}(71, \cdot)\) None 0 4
225.1.o \(\chi_{225}(7, \cdot)\) None 0 4
225.1.r \(\chi_{225}(28, \cdot)\) None 0 8
225.1.t \(\chi_{225}(11, \cdot)\) None 0 8
225.1.v \(\chi_{225}(14, \cdot)\) None 0 8
225.1.x \(\chi_{225}(13, \cdot)\) None 0 16