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Properties

Label 2310.2.bf
Level $2310$
Weight $2$
Character orbit 2310.bf
Rep. character $\chi_{2310}(529,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1184 160 1024
Cusp forms 1120 160 960
Eisenstein series 64 0 64

Trace form

\( 160 q + 80 q^{4} + 80 q^{9} + O(q^{10}) \) \( 160 q + 80 q^{4} + 80 q^{9} - 80 q^{16} - 16 q^{19} - 16 q^{21} + 16 q^{25} + 96 q^{29} - 16 q^{31} + 64 q^{34} + 16 q^{35} + 160 q^{36} - 16 q^{39} + 64 q^{41} + 32 q^{49} - 32 q^{50} + 16 q^{59} + 16 q^{61} - 160 q^{64} + 48 q^{65} + 16 q^{66} + 64 q^{69} + 24 q^{70} - 48 q^{74} + 8 q^{75} - 32 q^{76} - 32 q^{79} - 80 q^{81} - 32 q^{84} - 80 q^{85} - 16 q^{86} - 32 q^{89} + 48 q^{91} + 32 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1155, [\chi])\)\(^{\oplus 2}\)