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Properties

Label 2280.2.fn
Level $2280$
Weight $2$
Character orbit 2280.fn
Rep. character $\chi_{2280}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2880$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2280.fn (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2280, [\chi])\).

Total New Old
Modular forms 5856 2880 2976
Cusp forms 5664 2880 2784
Eisenstein series 192 0 192

Trace form

\( 2880 q + 12 q^{6} + O(q^{10}) \) \( 2880 q + 12 q^{6} + 12 q^{16} - 120 q^{20} + 72 q^{28} + 60 q^{32} - 12 q^{36} - 204 q^{38} - 60 q^{40} - 144 q^{47} + 144 q^{58} + 120 q^{62} + 72 q^{72} + 72 q^{76} + 72 q^{78} - 120 q^{80} + 192 q^{82} - 36 q^{90} + 240 q^{92} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2280, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)