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Properties

Label 1440.2.bt
Level $1440$
Weight $2$
Character orbit 1440.bt
Rep. character $\chi_{1440}(239,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $136$
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.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 608 152 456
Cusp forms 544 136 408
Eisenstein series 64 16 48

Trace form

\( 136 q - 8 q^{9} + O(q^{10}) \) \( 136 q - 8 q^{9} + 12 q^{11} + 16 q^{19} - 2 q^{25} - 12 q^{41} - 48 q^{49} + 32 q^{51} + 12 q^{59} - 6 q^{65} - 46 q^{75} - 40 q^{91} + 76 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)