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Properties

Label 1120.2.ct
Level $1120$
Weight $2$
Character orbit 1120.ct
Rep. character $\chi_{1120}(29,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $576$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1120.ct (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1120, [\chi])\).

Total New Old
Modular forms 784 576 208
Cusp forms 752 576 176
Eisenstein series 32 0 32

Trace form

\( 576 q + O(q^{10}) \) \( 576 q + 16 q^{24} - 80 q^{26} + 40 q^{30} - 80 q^{36} + 40 q^{40} + 104 q^{50} + 32 q^{51} - 64 q^{54} - 64 q^{55} + 48 q^{56} + 8 q^{60} - 64 q^{61} - 64 q^{66} + 64 q^{69} - 48 q^{70} - 48 q^{74} - 64 q^{75} - 80 q^{80} - 64 q^{86} - 120 q^{90} - 288 q^{94} - 64 q^{96} + 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1120, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)