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Properties

Label 2240.4.dg
Level $2240$
Weight $4$
Character orbit 2240.dg
Rep. character $\chi_{2240}(271,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $768$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2240.dg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2240, [\chi])\).

Total New Old
Modular forms 4672 768 3904
Cusp forms 4544 768 3776
Eisenstein series 128 0 128

Trace form

\( 768 q + O(q^{10}) \) \( 768 q + 40 q^{11} - 656 q^{23} - 800 q^{29} + 16 q^{37} + 1616 q^{43} + 1400 q^{51} - 752 q^{53} - 2064 q^{59} - 2040 q^{67} + 448 q^{71} + 31104 q^{81} + 4448 q^{91} + 3600 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2240, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)