Properties

Label 1225.1.q
Level $1225$
Weight $1$
Character orbit 1225.q
Rep. character $\chi_{1225}(18,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $12$
Newform subspaces $2$
Sturm bound $140$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1225.q (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(140\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 108 28 80
Cusp forms 12 12 0
Eisenstein series 96 16 80

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q + O(q^{10}) \) \( 12q + 6q^{16} - 12q^{36} - 12q^{46} + 6q^{81} - 12q^{86} + O(q^{100}) \)

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.q.a \(4\) \(0.611\) \(\Q(\zeta_{12})\) \(D_{2}\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{4}-\zeta_{12}^{5}q^{9}+\zeta_{12}^{4}q^{11}+\cdots\)
1225.1.q.b \(8\) \(0.611\) \(\Q(\zeta_{24})\) \(D_{6}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)