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Properties

Label 2340.2.fd
Level $2340$
Weight $2$
Character orbit 2340.fd
Rep. character $\chi_{2340}(127,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $824$
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.fd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
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 2080 856 1224
Cusp forms 1952 824 1128
Eisenstein series 128 32 96

Trace form

\( 824 q + 6 q^{2} + O(q^{10}) \) \( 824 q + 6 q^{2} - 10 q^{10} - 6 q^{13} + 4 q^{16} - 6 q^{17} + 30 q^{20} + 4 q^{22} - 36 q^{25} + 16 q^{26} - 6 q^{28} - 24 q^{32} - 6 q^{37} + 16 q^{38} - 44 q^{40} + 24 q^{41} - 12 q^{46} + 90 q^{50} - 10 q^{52} + 20 q^{53} - 12 q^{56} - 78 q^{58} - 8 q^{61} - 32 q^{62} - 28 q^{65} + 44 q^{68} - 12 q^{76} - 40 q^{77} - 24 q^{80} + 38 q^{82} - 12 q^{85} + 22 q^{88} + 84 q^{92} - 12 q^{97} + 162 q^{98} + O(q^{100}) \)

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

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