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Properties

Label 1320.2.bi
Level $1320$
Weight $2$
Character orbit 1320.bi
Rep. character $\chi_{1320}(373,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1320.bi (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1320, [\chi])\).

Total New Old
Modular forms 592 288 304
Cusp forms 560 288 272
Eisenstein series 32 0 32

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 16 q^{12} - 16 q^{16} + 40 q^{20} - 12 q^{22} - 16 q^{26} - 56 q^{38} + 112 q^{56} + 32 q^{58} - 24 q^{66} - 64 q^{71} - 24 q^{78} - 40 q^{80} - 288 q^{81} - 24 q^{82} - 80 q^{86} + 36 q^{88} + 32 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1320, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)