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Properties

Label 2400.2.bp
Level $2400$
Weight $2$
Character orbit 2400.bp
Rep. character $\chi_{2400}(43,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $576$
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.bp (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
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 576 1392
Cusp forms 1872 576 1296
Eisenstein series 96 0 96

Trace form

\( 576 q - 24 q^{8} + O(q^{10}) \) \( 576 q - 24 q^{8} - 16 q^{12} + 32 q^{19} - 16 q^{22} - 40 q^{32} + 16 q^{34} - 56 q^{38} + 40 q^{42} - 32 q^{43} + 64 q^{44} + 32 q^{48} - 576 q^{49} + 32 q^{51} - 88 q^{52} - 48 q^{56} - 32 q^{58} - 64 q^{61} + 72 q^{62} - 48 q^{64} + 96 q^{66} + 48 q^{67} + 56 q^{68} + 128 q^{71} + 144 q^{76} - 48 q^{78} + 120 q^{82} - 80 q^{83} + 128 q^{86} + 104 q^{88} + 72 q^{92} - 128 q^{94} - 64 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)