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Properties

Label 1120.2.db
Level $1120$
Weight $2$
Character orbit 1120.db
Rep. character $\chi_{1120}(207,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $176$
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.db (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 832 208 624
Cusp forms 704 176 528
Eisenstein series 128 32 96

Trace form

\( 176 q + 4 q^{3} + O(q^{10}) \) \( 176 q + 4 q^{3} + 8 q^{11} - 4 q^{17} - 4 q^{25} + 40 q^{27} + 20 q^{33} + 32 q^{35} - 32 q^{41} + 16 q^{43} + 8 q^{51} - 40 q^{57} - 4 q^{65} + 28 q^{67} - 4 q^{73} + 4 q^{75} + 32 q^{81} + 16 q^{83} - 16 q^{91} - 48 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)