Properties

Label 225.1.g
Level 225
Weight 1
Character orbit g
Rep. character \(\chi_{225}(82,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 2
Newform subspaces 1
Sturm bound 30
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 225.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(225, [\chi])\).

Total New Old
Modular forms 26 4 22
Cusp forms 2 2 0
Eisenstein series 24 2 22

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 \(S_{1}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
225.1.g.a \(2\) \(0.112\) \(\Q(\sqrt{-1}) \) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots\)

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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