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Properties

Label 1120.2.cg
Level $1120$
Weight $2$
Character orbit 1120.cg
Rep. character $\chi_{1120}(141,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $384$
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.cg (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
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 784 384 400
Cusp forms 752 384 368
Eisenstein series 32 0 32

Trace form

\( 384 q + O(q^{10}) \) \( 384 q + 16 q^{10} + 40 q^{16} + 40 q^{18} - 8 q^{22} + 16 q^{23} + 16 q^{24} + 96 q^{27} - 80 q^{32} - 80 q^{34} + 48 q^{36} + 96 q^{39} + 16 q^{43} - 8 q^{44} + 128 q^{46} - 32 q^{51} + 128 q^{52} + 32 q^{53} - 64 q^{54} - 8 q^{56} - 144 q^{58} + 64 q^{61} - 48 q^{62} - 80 q^{63} + 64 q^{66} - 80 q^{67} - 96 q^{68} + 64 q^{69} - 144 q^{72} - 8 q^{74} + 32 q^{77} - 48 q^{78} - 64 q^{80} - 144 q^{86} - 160 q^{88} + 8 q^{92} - 16 q^{94} + 128 q^{95} + 64 q^{96} + 128 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)