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Properties

Label 2240.2.r
Level $2240$
Weight $2$
Character orbit 2240.r
Rep. character $\chi_{2240}(433,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $184$
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.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 800 200 600
Cusp forms 736 184 552
Eisenstein series 64 16 48

Trace form

\( 184 q - 168 q^{9} + O(q^{10}) \) \( 184 q - 168 q^{9} + 8 q^{11} + 8 q^{15} - 4 q^{21} - 20 q^{35} - 8 q^{37} - 48 q^{39} + 8 q^{51} + 24 q^{57} + 32 q^{63} - 8 q^{65} + 104 q^{81} + 16 q^{85} + 20 q^{91} + 16 q^{93} + 56 q^{95} - 24 q^{99} + O(q^{100}) \)

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

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