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Properties

Label 1440.2.cs
Level $1440$
Weight $2$
Character orbit 1440.cs
Rep. character $\chi_{1440}(163,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $472$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.cs (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1440, [\chi])\).

Total New Old
Modular forms 1184 488 696
Cusp forms 1120 472 648
Eisenstein series 64 16 48

Trace form

\( 472 q + 4 q^{2} + 4 q^{5} - 8 q^{7} + 16 q^{8} + O(q^{10}) \) \( 472 q + 4 q^{2} + 4 q^{5} - 8 q^{7} + 16 q^{8} + 8 q^{10} + 8 q^{11} - 4 q^{13} + 16 q^{14} - 8 q^{16} + 16 q^{19} + 32 q^{20} + 12 q^{22} + 8 q^{23} - 4 q^{25} + 8 q^{26} - 20 q^{28} + 24 q^{32} + 8 q^{34} - 4 q^{37} + 60 q^{38} + 16 q^{40} + 8 q^{41} - 36 q^{43} - 16 q^{44} - 8 q^{46} + 8 q^{47} + 424 q^{49} - 4 q^{50} + 16 q^{52} + 4 q^{53} - 36 q^{55} + 56 q^{56} + 28 q^{58} + 24 q^{61} - 40 q^{62} - 48 q^{64} + 8 q^{65} - 28 q^{67} + 48 q^{68} + 4 q^{70} + 40 q^{71} + 40 q^{76} + 32 q^{77} + 88 q^{80} - 12 q^{82} + 44 q^{83} - 4 q^{85} + 40 q^{86} + 8 q^{88} - 8 q^{91} - 20 q^{92} + 32 q^{94} - 8 q^{97} + 96 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)