Properties

Label 1320.2.bt
Level $1320$
Weight $2$
Character orbit 1320.bt
Rep. character $\chi_{1320}(923,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $560$
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.bt (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1320 \)
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 592 592 0
Cusp forms 560 560 0
Eisenstein series 32 32 0

Trace form

\( 560 q - 8 q^{3} + O(q^{10}) \) \( 560 q - 8 q^{3} + 8 q^{12} - 16 q^{16} - 4 q^{22} - 16 q^{25} - 8 q^{27} + 8 q^{33} + 56 q^{36} - 32 q^{42} - 16 q^{48} + 40 q^{60} - 40 q^{66} - 16 q^{67} + 32 q^{70} - 8 q^{75} - 24 q^{78} - 16 q^{81} - 8 q^{82} - 92 q^{88} - 32 q^{91} - 48 q^{97} + O(q^{100}) \)

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

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