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Properties

Label 2400.2.bw
Level $2400$
Weight $2$
Character orbit 2400.bw
Rep. character $\chi_{2400}(301,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $608$
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.bw (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
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 608 1360
Cusp forms 1872 608 1264
Eisenstein series 96 0 96

Trace form

\( 608 q + O(q^{10}) \) \( 608 q + 16 q^{12} + 32 q^{14} - 8 q^{16} - 8 q^{18} + 24 q^{22} - 16 q^{23} + 8 q^{24} - 40 q^{26} + 40 q^{28} + 48 q^{31} + 40 q^{32} + 40 q^{34} + 40 q^{38} - 16 q^{43} + 8 q^{44} - 32 q^{46} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 8 q^{54} + 104 q^{56} + 32 q^{58} - 64 q^{59} + 32 q^{61} + 48 q^{62} + 16 q^{63} - 24 q^{64} - 48 q^{66} + 16 q^{67} + 104 q^{68} + 32 q^{69} - 64 q^{71} + 192 q^{74} + 56 q^{76} - 32 q^{77} + 24 q^{78} + 40 q^{82} + 64 q^{86} + 128 q^{88} - 48 q^{91} + 64 q^{92} + 144 q^{94} + 40 q^{96} - 32 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)