Properties

Label 3600.2.eq
Level $3600$
Weight $2$
Character orbit 3600.eq
Rep. character $\chi_{3600}(611,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1920$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3600.eq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1200 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3600, [\chi])\).

Total New Old
Modular forms 5824 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

Trace form

\( 1920 q + O(q^{10}) \) \( 1920 q + 32 q^{22} - 64 q^{34} - 72 q^{40} + 64 q^{43} + 1920 q^{49} - 32 q^{52} + 64 q^{55} - 64 q^{58} + 72 q^{70} + 48 q^{76} - 80 q^{82} - 32 q^{88} - 40 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)