↑

Properties

Label 2340.2.bz
Level $2340$
Weight $2$
Character orbit 2340.bz
Rep. character $\chi_{2340}(1681,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
Sturm bound $1008$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2340.bz (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2340, [\chi])\).

Total New Old
Modular forms 1032 112 920
Cusp forms 984 112 872
Eisenstein series 48 0 48

Trace form

\( 112 q - 2 q^{9} + O(q^{10}) \) \( 112 q - 2 q^{9} + 2 q^{13} + 16 q^{17} + 6 q^{19} - 6 q^{21} + 56 q^{25} - 12 q^{27} + 10 q^{29} + 12 q^{31} - 18 q^{33} - 8 q^{35} - 6 q^{37} + 26 q^{39} + 8 q^{43} - 36 q^{47} - 104 q^{49} - 8 q^{51} + 32 q^{53} - 18 q^{57} + 24 q^{59} + 28 q^{61} + 4 q^{65} + 8 q^{69} + 36 q^{71} + 40 q^{77} - 8 q^{79} - 14 q^{81} + 18 q^{83} + 18 q^{85} + 64 q^{87} + 36 q^{89} + 12 q^{91} - 30 q^{93} + 4 q^{95} + 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2340, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2340, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)