Properties

Label 1225.1.i
Level $1225$
Weight $1$
Character orbit 1225.i
Rep. character $\chi_{1225}(276,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $140$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1225.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(140\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1225, [\chi])\).

Total New Old
Modular forms 52 16 36
Cusp forms 4 4 0
Eisenstein series 48 12 36

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

\( 4q - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{9} + 2q^{11} + 2q^{16} - 4q^{29} - 2q^{46} + 4q^{64} - 4q^{71} - 2q^{74} + 2q^{79} - 2q^{81} - 2q^{86} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1225, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1225.1.i.a \(2\) \(0.611\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots\)
1225.1.i.b \(2\) \(0.611\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots\)