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Properties

Label 2240.4.bc
Level $2240$
Weight $4$
Character orbit 2240.bc
Rep. character $\chi_{2240}(111,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $384$
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.bc (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(i)\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 2336 384 1952
Cusp forms 2272 384 1888
Eisenstein series 64 0 64

Trace form

\( 384 q + O(q^{10}) \) \( 384 q - 40 q^{11} + 656 q^{23} - 400 q^{29} - 16 q^{37} + 808 q^{43} + 2800 q^{51} + 752 q^{53} + 2040 q^{67} - 448 q^{71} - 31104 q^{81} - 4448 q^{91} + 1800 q^{99} + O(q^{100}) \)

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

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