Properties

Label 225.1
Level 225
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 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: \( 1 \)
Newform subspaces: \( 1 \)
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

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

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + T^{4} \)
$3$ 1
$5$ 1
$7$ \( 1 + T^{4} \)
$11$ \( ( 1 + T^{2} )^{2} \)
$13$ \( 1 + T^{4} \)
$17$ \( 1 + T^{4} \)
$19$ \( ( 1 + T^{2} )^{2} \)
$23$ \( 1 + T^{4} \)
$29$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$31$ \( ( 1 + T )^{4} \)
$37$ \( 1 + T^{4} \)
$41$ \( ( 1 + T^{2} )^{2} \)
$43$ \( 1 + T^{4} \)
$47$ \( 1 + T^{4} \)
$53$ \( 1 + T^{4} \)
$59$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$61$ \( ( 1 - T )^{4} \)
$67$ \( 1 + T^{4} \)
$71$ \( ( 1 + T^{2} )^{2} \)
$73$ \( 1 + T^{4} \)
$79$ \( ( 1 + T^{2} )^{2} \)
$83$ \( 1 + T^{4} \)
$89$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$97$ \( 1 + T^{4} \)
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