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Properties

Label 2340.2.bb
Level $2340$
Weight $2$
Character orbit 2340.bb
Rep. character $\chi_{2340}(703,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $360$
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.bb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
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 360 680
Cusp forms 976 360 616
Eisenstein series 64 0 64

Trace form

\( 360 q - 12 q^{8} + O(q^{10}) \) \( 360 q - 12 q^{8} + 8 q^{10} + 8 q^{16} + 8 q^{22} + 44 q^{28} + 40 q^{32} + 44 q^{38} + 8 q^{40} - 40 q^{46} - 40 q^{50} - 8 q^{52} + 48 q^{53} - 104 q^{56} + 4 q^{58} + 64 q^{61} - 60 q^{62} - 16 q^{68} - 12 q^{70} + 16 q^{73} + 24 q^{76} + 48 q^{77} + 100 q^{80} + 20 q^{82} + 48 q^{85} + 48 q^{86} + 28 q^{88} + 116 q^{92} + 80 q^{97} - 32 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)