Properties

Label 225.1.g
Level $225$
Weight $1$
Character orbit 225.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

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

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

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
225.1.g.a 225.g 5.c $2$ $0.112$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{5}) \) 225.1.g.a \(0\) \(0\) \(0\) \(0\) \(q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots\)