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Properties

Label 2310.2.bu
Level $2310$
Weight $2$
Character orbit 2310.bu
Rep. character $\chi_{2310}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $576$
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.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 2368 576 1792
Cusp forms 2240 576 1664
Eisenstein series 128 0 128

Trace form

\( 576 q + 144 q^{4} - 4 q^{9} + O(q^{10}) \) \( 576 q + 144 q^{4} - 4 q^{9} - 8 q^{15} - 144 q^{16} + 60 q^{25} + 60 q^{30} + 32 q^{31} - 16 q^{34} - 16 q^{36} - 20 q^{39} - 24 q^{45} + 40 q^{46} - 144 q^{49} + 20 q^{51} + 48 q^{55} + 8 q^{60} + 144 q^{64} + 40 q^{66} + 96 q^{69} - 8 q^{70} - 40 q^{75} + 40 q^{79} - 4 q^{81} + 20 q^{84} - 20 q^{85} + 100 q^{90} - 72 q^{91} + 152 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1155, [\chi])\)\(^{\oplus 2}\)