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Properties

Label 1320.2.cz
Level $1320$
Weight $2$
Character orbit 1320.cz
Rep. character $\chi_{1320}(251,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $768$
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.cz (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 264 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1184 768 416
Cusp forms 1120 768 352
Eisenstein series 64 0 64

Trace form

\( 768 q + O(q^{10}) \) \( 768 q + 32 q^{16} + 32 q^{22} - 16 q^{24} - 192 q^{25} - 72 q^{28} + 16 q^{30} + 8 q^{33} - 24 q^{34} + 44 q^{36} + 46 q^{42} + 86 q^{48} + 192 q^{49} - 8 q^{52} + 48 q^{54} + 16 q^{57} + 16 q^{58} - 42 q^{60} - 60 q^{64} + 126 q^{66} + 128 q^{67} + 36 q^{70} - 8 q^{72} - 144 q^{76} + 28 q^{78} - 16 q^{81} - 12 q^{82} - 72 q^{84} - 28 q^{88} + 144 q^{91} - 24 q^{94} + 26 q^{96} - 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)