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Properties

Label 1440.2.dw
Level $1440$
Weight $2$
Character orbit 1440.dw
Rep. character $\chi_{1440}(61,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1536$
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.dw (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 288 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2336 1536 800
Cusp forms 2272 1536 736
Eisenstein series 64 0 64

Trace form

\( 1536 q + O(q^{10}) \) \( 1536 q + 80 q^{24} + 48 q^{27} + 24 q^{36} + 48 q^{39} + 160 q^{42} + 176 q^{44} + 88 q^{54} + 160 q^{56} + 72 q^{58} + 48 q^{62} - 64 q^{66} - 24 q^{76} - 24 q^{78} - 64 q^{80} - 80 q^{83} - 56 q^{84} - 208 q^{86} - 72 q^{90} + 128 q^{95} - 104 q^{96} - 272 q^{98} + 64 q^{99} + O(q^{100}) \)

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

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