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Properties

Label 2280.2.cr
Level $2280$
Weight $2$
Character orbit 2280.cr
Rep. character $\chi_{2280}(1261,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.cr (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 976 320 656
Cusp forms 944 320 624
Eisenstein series 32 0 32

Trace form

\( 320 q + 2 q^{4} + 2 q^{6} + 160 q^{9} + O(q^{10}) \) \( 320 q + 2 q^{4} + 2 q^{6} + 160 q^{9} - 2 q^{10} + 8 q^{15} - 2 q^{16} + 4 q^{24} + 160 q^{25} - 40 q^{26} + 40 q^{28} - 16 q^{31} + 60 q^{32} - 14 q^{34} - 2 q^{36} - 60 q^{38} - 4 q^{40} + 20 q^{44} - 48 q^{46} + 16 q^{48} + 288 q^{49} + 4 q^{52} - 2 q^{54} + 16 q^{56} + 16 q^{57} + 24 q^{58} + 2 q^{60} + 72 q^{62} + 80 q^{64} + 40 q^{66} + 104 q^{68} + 12 q^{70} - 16 q^{73} + 32 q^{74} + 20 q^{76} + 20 q^{78} + 16 q^{79} + 16 q^{80} - 160 q^{81} + 36 q^{82} + 48 q^{84} + 60 q^{86} + 144 q^{88} + 2 q^{90} + 24 q^{92} + 20 q^{94} + 36 q^{96} - 32 q^{97} - 8 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)