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Properties

Label 1332.2.cs
Level $1332$
Weight $2$
Character orbit 1332.cs
Rep. character $\chi_{1332}(215,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $456$
Sturm bound $456$

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Defining parameters

Level: \( N \) \(=\) \( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1332.cs (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 444 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1332, [\chi])\).

Total New Old
Modular forms 1416 456 960
Cusp forms 1320 456 864
Eisenstein series 96 0 96

Trace form

\( 456 q + O(q^{10}) \) \( 456 q + 48 q^{13} + 12 q^{16} - 12 q^{22} + 12 q^{28} - 24 q^{37} - 60 q^{40} + 36 q^{46} - 72 q^{49} - 60 q^{52} - 72 q^{58} - 24 q^{61} + 204 q^{70} + 12 q^{76} + 180 q^{82} - 12 q^{85} + 72 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1332, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1332, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1332, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 2}\)