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Properties

Label 2280.2.ef
Level $2280$
Weight $2$
Character orbit 2280.ef
Rep. character $\chi_{2280}(41,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $480$
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.ef (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 2976 480 2496
Cusp forms 2784 480 2304
Eisenstein series 192 0 192

Trace form

\( 480 q + 6 q^{3} + 18 q^{9} + O(q^{10}) \) \( 480 q + 6 q^{3} + 18 q^{9} - 12 q^{13} - 12 q^{19} - 18 q^{27} - 18 q^{33} - 72 q^{39} + 84 q^{43} - 240 q^{49} - 18 q^{51} + 24 q^{61} + 48 q^{67} + 228 q^{73} + 42 q^{81} + 36 q^{87} + 120 q^{91} - 60 q^{97} + 12 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 2}\)