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Properties

Label 1120.2.ef
Level $1120$
Weight $2$
Character orbit 1120.ef
Rep. character $\chi_{1120}(221,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1024$
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.ef (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 1568 1024 544
Cusp forms 1504 1024 480
Eisenstein series 64 0 64

Trace form

\( 1024 q + O(q^{10}) \) \( 1024 q - 32 q^{14} + 40 q^{16} + 40 q^{18} + 32 q^{20} + 16 q^{22} + 16 q^{23} - 80 q^{24} - 40 q^{28} - 80 q^{38} + 40 q^{42} - 32 q^{43} - 96 q^{44} + 48 q^{52} + 32 q^{53} + 176 q^{54} + 80 q^{56} + 32 q^{59} - 96 q^{64} + 48 q^{66} - 80 q^{67} - 64 q^{71} - 8 q^{74} - 96 q^{78} + 160 q^{83} - 56 q^{84} - 144 q^{90} + 96 q^{91} - 16 q^{92} - 48 q^{94} + 136 q^{96} - 248 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)