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Properties

Label 2268.4.be
Level $2268$
Weight $4$
Character orbit 2268.be
Rep. character $\chi_{2268}(1619,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1136$
Sturm bound $1728$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2268.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2268, [\chi])\).

Total New Old
Modular forms 2640 1168 1472
Cusp forms 2544 1136 1408
Eisenstein series 96 32 64

Trace form

\( 1136 q + 2 q^{4} + O(q^{10}) \) \( 1136 q + 2 q^{4} + 28 q^{10} + 16 q^{13} + 182 q^{16} + 144 q^{22} + 13404 q^{25} + 120 q^{28} + 40 q^{34} - 8 q^{37} - 248 q^{40} + 864 q^{46} + 8 q^{49} - 254 q^{52} + 1366 q^{58} + 4 q^{61} - 16 q^{64} + 5142 q^{70} - 8 q^{73} - 3408 q^{76} + 2356 q^{82} + 1016 q^{85} + 3438 q^{88} + 66 q^{94} + 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2268, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2268, [\chi])\) into lower level spaces

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