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Properties

Label 2400.2.dy
Level $2400$
Weight $2$
Character orbit 2400.dy
Rep. character $\chi_{2400}(11,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $7616$
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.dy (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2400 \)
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 7744 0
Cusp forms 7616 7616 0
Eisenstein series 128 128 0

Trace form

\( 7616 q - 12 q^{3} - 24 q^{4} - 12 q^{6} - 64 q^{7} - 12 q^{9} + O(q^{10}) \) \( 7616 q - 12 q^{3} - 24 q^{4} - 12 q^{6} - 64 q^{7} - 12 q^{9} - 32 q^{10} - 12 q^{12} - 24 q^{13} - 32 q^{15} - 24 q^{16} - 32 q^{18} - 24 q^{19} - 12 q^{21} + 8 q^{22} - 32 q^{24} - 32 q^{25} - 12 q^{27} - 24 q^{28} - 64 q^{30} - 24 q^{33} + 8 q^{34} + 108 q^{36} - 24 q^{37} - 12 q^{39} - 64 q^{40} - 12 q^{42} - 64 q^{43} - 16 q^{45} - 24 q^{46} + 144 q^{48} - 8 q^{51} - 24 q^{52} - 12 q^{54} - 64 q^{55} - 32 q^{57} - 88 q^{58} + 112 q^{60} - 24 q^{61} - 24 q^{64} - 28 q^{66} - 24 q^{67} - 12 q^{69} - 80 q^{70} + 108 q^{72} - 24 q^{73} - 16 q^{75} - 64 q^{76} + 140 q^{78} - 48 q^{79} + 16 q^{82} + 140 q^{84} + 8 q^{85} - 124 q^{87} - 24 q^{88} + 44 q^{90} - 24 q^{91} - 56 q^{93} - 16 q^{94} - 12 q^{96} - 48 q^{97} - 32 q^{99} + O(q^{100}) \)

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.