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Properties

Label 1440.2.cl
Level $1440$
Weight $2$
Character orbit 1440.cl
Rep. character $\chi_{1440}(181,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $320$
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.cl (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
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 320 864
Cusp forms 1120 320 800
Eisenstein series 64 0 64

Trace form

\( 320 q + O(q^{10}) \) \( 320 q + 8 q^{10} - 16 q^{14} - 8 q^{16} - 16 q^{20} + 8 q^{22} - 16 q^{23} + 40 q^{28} + 40 q^{32} + 40 q^{34} + 40 q^{38} - 16 q^{43} + 96 q^{44} + 64 q^{46} + 16 q^{52} - 32 q^{53} + 88 q^{56} + 72 q^{58} + 32 q^{59} + 32 q^{61} + 72 q^{62} - 48 q^{64} + 16 q^{67} + 48 q^{68} + 32 q^{71} + 8 q^{74} - 16 q^{76} - 32 q^{77} - 32 q^{80} + 80 q^{83} - 136 q^{86} - 80 q^{88} + 96 q^{91} - 8 q^{92} + 40 q^{94} + 64 q^{95} - 192 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)