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Properties

Label 2240.2.fi
Level $2240$
Weight $2$
Character orbit 2240.fi
Rep. character $\chi_{2240}(221,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $4096$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.fi (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 448 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2240, [\chi])\).

Total New Old
Modular forms 6208 4096 2112
Cusp forms 6080 4096 1984
Eisenstein series 128 0 128

Trace form

\( 4096 q + O(q^{10}) \) \( 4096 q - 32 q^{22} + 160 q^{24} + 80 q^{28} + 160 q^{38} + 80 q^{42} + 16 q^{44} + 96 q^{52} - 64 q^{59} - 192 q^{64} + 96 q^{66} + 160 q^{67} + 128 q^{71} - 16 q^{74} - 192 q^{78} + 112 q^{84} + 288 q^{90} - 272 q^{96} + 272 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2240, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)