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Properties

Label 2240.2.bw
Level $2240$
Weight $2$
Character orbit 2240.bw
Rep. character $\chi_{2240}(1089,\cdot)$
Character field $\Q(\zeta_{6})$
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.bw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 816 200 616
Cusp forms 720 184 536
Eisenstein series 96 16 80

Trace form

\( 184 q + 2 q^{5} + 80 q^{9} + O(q^{10}) \) \( 184 q + 2 q^{5} + 80 q^{9} + 20 q^{21} - 2 q^{25} + 16 q^{29} - 16 q^{41} - 24 q^{45} - 8 q^{49} + 4 q^{61} + 8 q^{65} + 40 q^{69} - 36 q^{81} + 76 q^{85} - 20 q^{89} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)