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Properties

Label 2400.2.bt
Level $2400$
Weight $2$
Character orbit 2400.bt
Rep. character $\chi_{2400}(299,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1136$
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.bt (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 480 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1968 1168 800
Cusp forms 1872 1136 736
Eisenstein series 96 32 64

Trace form

\( 1136 q + 16 q^{4} - 8 q^{6} + 8 q^{9} + O(q^{10}) \) \( 1136 q + 16 q^{4} - 8 q^{6} + 8 q^{9} - 16 q^{16} + 16 q^{19} - 8 q^{21} + 8 q^{24} + 48 q^{34} + 72 q^{36} + 8 q^{39} - 16 q^{46} - 32 q^{51} + 8 q^{54} + 48 q^{61} + 112 q^{64} + 72 q^{66} + 8 q^{69} - 128 q^{76} + 96 q^{79} + 48 q^{84} - 16 q^{91} + 48 q^{94} + 56 q^{96} + 136 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)