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Properties

Label 1320.2.cx
Level $1320$
Weight $2$
Character orbit 1320.cx
Rep. character $\chi_{1320}(19,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $576$
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.cx (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
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 576 608
Cusp forms 1120 576 544
Eisenstein series 64 0 64

Trace form

\( 576 q + 144 q^{9} + O(q^{10}) \) \( 576 q + 144 q^{9} + 8 q^{14} - 16 q^{16} + 30 q^{20} + 68 q^{26} - 20 q^{30} + 32 q^{34} + 70 q^{40} + 68 q^{44} - 120 q^{46} + 144 q^{49} + 70 q^{50} + 16 q^{56} + 32 q^{59} + 12 q^{60} + 60 q^{64} - 20 q^{66} + 56 q^{70} + 48 q^{75} - 74 q^{80} - 144 q^{81} + 16 q^{86} - 20 q^{90} + 32 q^{91} - 140 q^{94} + O(q^{100}) \)

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

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