Properties

Label 900.1.m
Level 900
Weight 1
Character orbit m
Rep. character \(\chi_{900}(107,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newforms 1
Sturm bound 180
Trace bound 0

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Defining parameters

Level: \( N \) = \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 900.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 60 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(900, [\chi])\).

Total New Old
Modular forms 68 4 64
Cusp forms 20 4 16
Eisenstein series 48 0 48

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

\( 4q + O(q^{10}) \) \( 4q + 4q^{13} - 4q^{16} + 4q^{37} - 4q^{52} - 4q^{58} - 4q^{73} + 4q^{82} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(900, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
900.1.m.a \(4\) \(0.449\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{8}+(1-\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)