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Properties

Label 1440.2.cn
Level $1440$
Weight $2$
Character orbit 1440.cn
Rep. character $\chi_{1440}(251,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $256$
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.cn (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
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 256 928
Cusp forms 1120 256 864
Eisenstein series 64 0 64

Trace form

\( 256 q + O(q^{10}) \) \( 256 q - 16 q^{10} - 32 q^{16} + 128 q^{46} + 224 q^{52} - 64 q^{61} + 96 q^{64} + 64 q^{67} + 16 q^{76} + 64 q^{79} - 160 q^{88} + 192 q^{91} - 112 q^{94} + O(q^{100}) \)

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

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