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Properties

Label 2310.2.de
Level $2310$
Weight $2$
Character orbit 2310.de
Rep. character $\chi_{2310}(289,\cdot)$
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.de (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

\( 768 q - 96 q^{4} + 8 q^{5} - 16 q^{6} - 96 q^{9} + O(q^{10}) \) \( 768 q - 96 q^{4} + 8 q^{5} - 16 q^{6} - 96 q^{9} + 4 q^{10} - 4 q^{11} - 12 q^{14} + 12 q^{15} + 96 q^{16} - 24 q^{19} + 16 q^{20} - 8 q^{24} + 16 q^{25} + 8 q^{26} - 8 q^{30} + 12 q^{31} + 64 q^{35} - 192 q^{36} + 6 q^{40} + 120 q^{41} - 36 q^{44} - 8 q^{45} + 24 q^{46} + 8 q^{49} - 24 q^{51} + 32 q^{54} - 60 q^{55} + 16 q^{56} + 16 q^{59} - 4 q^{60} + 120 q^{61} + 192 q^{64} - 104 q^{65} + 32 q^{69} - 82 q^{70} + 192 q^{71} - 8 q^{74} + 8 q^{75} + 112 q^{76} - 8 q^{79} - 12 q^{80} + 96 q^{81} - 96 q^{85} + 72 q^{86} + 16 q^{89} + 8 q^{90} + 196 q^{91} - 52 q^{94} - 76 q^{95} + 8 q^{96} - 8 q^{99} + O(q^{100}) \)

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

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