↑

Properties

Label 2240.2.dr
Level $2240$
Weight $2$
Character orbit 2240.dr
Rep. character $\chi_{2240}(1103,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $368$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.dr (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1600 400 1200
Cusp forms 1472 368 1104
Eisenstein series 128 32 96

Trace form

\( 368 q - 2 q^{5} + 8 q^{7} + 168 q^{9} + O(q^{10}) \) \( 368 q - 2 q^{5} + 8 q^{7} + 168 q^{9} + 4 q^{11} - 16 q^{13} + 24 q^{15} - 4 q^{17} - 8 q^{21} + 4 q^{23} - 4 q^{33} + 6 q^{35} - 4 q^{37} + 16 q^{43} + 24 q^{45} + 24 q^{47} + 4 q^{51} + 16 q^{55} - 24 q^{57} + 16 q^{59} - 4 q^{61} + 12 q^{63} - 4 q^{65} - 20 q^{67} - 24 q^{69} + 96 q^{71} + 14 q^{75} - 128 q^{81} + 12 q^{85} + 4 q^{87} + 24 q^{91} - 28 q^{93} - 16 q^{97} + 24 q^{99} + O(q^{100}) \)

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

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