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Properties

Label 2340.2.bk
Level $2340$
Weight $2$
Character orbit 2340.bk
Rep. character $\chi_{2340}(883,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $412$
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.bk (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(i)\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 1040 428 612
Cusp forms 976 412 564
Eisenstein series 64 16 48

Trace form

\( 412 q + O(q^{10}) \) \( 412 q + 4 q^{10} - 6 q^{13} + 8 q^{16} - 12 q^{17} - 40 q^{22} + 12 q^{25} - 4 q^{26} - 4 q^{38} + 8 q^{40} + 4 q^{52} + 4 q^{53} + 24 q^{56} - 16 q^{61} - 4 q^{62} + 10 q^{65} + 40 q^{68} + 64 q^{77} - 44 q^{82} - 4 q^{88} + 36 q^{92} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)