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Properties

Label 2280.2.f
Level $2280$
Weight $2$
Character orbit 2280.f
Rep. character $\chi_{2280}(229,\cdot)$
Character field $\Q$
Dimension $216$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 488 216 272
Cusp forms 472 216 256
Eisenstein series 16 0 16

Trace form

\( 216 q + 216 q^{9} + O(q^{10}) \) \( 216 q + 216 q^{9} + 8 q^{10} + 16 q^{14} - 8 q^{25} + 16 q^{26} - 24 q^{30} - 48 q^{34} + 32 q^{39} + 4 q^{40} + 16 q^{41} - 32 q^{44} + 8 q^{46} - 216 q^{49} + 36 q^{50} + 32 q^{55} - 104 q^{56} + 20 q^{60} + 48 q^{64} + 48 q^{65} - 16 q^{66} - 76 q^{70} - 64 q^{71} - 40 q^{74} + 80 q^{80} + 216 q^{81} + 32 q^{84} + 32 q^{86} + 80 q^{89} + 8 q^{90} + 16 q^{94} + 40 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)