Properties

Label 2268.2.bf
Level $2268$
Weight $2$
Character orbit 2268.bf
Rep. character $\chi_{2268}(1459,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $368$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2268, [\chi])\).

Total New Old
Modular forms 912 400 512
Cusp forms 816 368 448
Eisenstein series 96 32 64

Trace form

\( 368 q + 2 q^{4} + O(q^{10}) \) \( 368 q + 2 q^{4} - 12 q^{10} + 14 q^{16} - 32 q^{22} + 156 q^{25} - 8 q^{37} + 36 q^{40} + 16 q^{46} + 8 q^{49} + 54 q^{52} + 6 q^{58} + 12 q^{61} - 16 q^{64} + 46 q^{70} - 24 q^{73} - 24 q^{82} + 56 q^{85} - 26 q^{88} + 6 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2268, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2268, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)