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Properties

Label 2268.2.bi
Level $2268$
Weight $2$
Character orbit 2268.bi
Rep. character $\chi_{2268}(55,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $376$
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.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
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 912 392 520
Cusp forms 816 376 440
Eisenstein series 96 16 80

Trace form

\( 376 q + 4 q^{4} + O(q^{10}) \) \( 376 q + 4 q^{4} + 4 q^{16} - 4 q^{22} + 180 q^{25} + 12 q^{28} - 16 q^{37} + 8 q^{46} + 4 q^{49} + 12 q^{58} - 8 q^{64} + 2 q^{70} - 32 q^{85} - 28 q^{88} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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