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Properties

Label 2310.2.df
Level $2310$
Weight $2$
Character orbit 2310.df
Rep. character $\chi_{2310}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2310.df (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2310, [\chi])\).

Total New Old
Modular forms 4736 768 3968
Cusp forms 4480 768 3712
Eisenstein series 256 0 256

Trace form

\( 768 q + 96 q^{4} - 24 q^{5} + 96 q^{9} + O(q^{10}) \) \( 768 q + 96 q^{4} - 24 q^{5} + 96 q^{9} - 4 q^{11} - 12 q^{14} - 12 q^{15} + 96 q^{16} + 24 q^{25} - 24 q^{26} - 36 q^{31} - 40 q^{35} - 192 q^{36} - 30 q^{40} + 36 q^{44} + 24 q^{45} - 40 q^{49} + 40 q^{51} - 16 q^{56} - 4 q^{60} + 120 q^{61} - 192 q^{64} - 66 q^{70} + 192 q^{71} + 24 q^{75} - 36 q^{80} + 96 q^{81} - 160 q^{85} + 72 q^{86} + 76 q^{91} - 60 q^{94} - 20 q^{95} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2310, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2310, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(770, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1155, [\chi])\)\(^{\oplus 2}\)