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Properties

Label 2310.2.bn
Level $2310$
Weight $2$
Character orbit 2310.bn
Rep. character $\chi_{2310}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
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 320 864
Cusp forms 1120 320 800
Eisenstein series 64 0 64

Trace form

\( 320 q - 160 q^{4} - 4 q^{9} + O(q^{10}) \) \( 320 q - 160 q^{4} - 4 q^{9} - 40 q^{15} - 160 q^{16} + 48 q^{19} - 20 q^{21} + 12 q^{24} + 20 q^{30} + 8 q^{36} - 16 q^{39} + 36 q^{45} + 24 q^{46} + 8 q^{49} + 24 q^{51} + 20 q^{60} + 120 q^{61} + 320 q^{64} - 24 q^{70} + 36 q^{75} + 16 q^{79} + 12 q^{81} - 32 q^{84} + 80 q^{85} - 16 q^{91} - 96 q^{94} - 12 q^{96} + O(q^{100}) \)

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

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