Properties

Label 3600.1.y
Level 3600
Weight 1
Character orbit y
Rep. character \(\chi_{3600}(793,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 0
Newforms 0
Sturm bound 720
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 3600.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 40 \)
Character field: \(\Q(i)\)
Newforms: \( 0 \)
Sturm bound: \(720\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3600, [\chi])\).

Total New Old
Modular forms 128 0 128
Cusp forms 32 0 32
Eisenstein series 96 0 96

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

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

Decomposition of \(S_{1}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)