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Properties

Label 2400.2.dx
Level $2400$
Weight $2$
Character orbit 2400.dx
Rep. character $\chi_{2400}(109,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $3840$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2400.dx (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 800 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2400, [\chi])\).

Total New Old
Modular forms 7744 3840 3904
Cusp forms 7616 3840 3776
Eisenstein series 128 0 128

Trace form

\( 3840 q + O(q^{10}) \) \( 3840 q + 80 q^{26} - 96 q^{31} + 48 q^{35} + 128 q^{40} + 24 q^{50} + 32 q^{55} + 48 q^{60} - 72 q^{64} + 120 q^{70} + 176 q^{74} + 32 q^{75} + 104 q^{80} + 440 q^{88} + 360 q^{92} + 152 q^{94} + 120 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2400, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)