Properties

Label 2340.2.hi
Level $2340$
Weight $2$
Character orbit 2340.hi
Rep. character $\chi_{2340}(853,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2340.hi (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 585 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 2064 336 1728
Cusp forms 1968 336 1632
Eisenstein series 96 0 96

Trace form

\( 336 q + O(q^{10}) \) \( 336 q + 4 q^{11} + 16 q^{15} + 4 q^{21} - 16 q^{23} + 12 q^{27} - 44 q^{33} - 24 q^{35} + 4 q^{39} + 8 q^{41} + 14 q^{45} + 168 q^{49} + 4 q^{57} + 16 q^{59} - 60 q^{63} - 20 q^{65} + 16 q^{69} + 16 q^{71} + 28 q^{75} + 16 q^{77} + 16 q^{81} + 24 q^{85} - 32 q^{87} + 48 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)