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Properties

Label 2365.2.r
Level $2365$
Weight $2$
Character orbit 2365.r
Rep. character $\chi_{2365}(694,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $440$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 215 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2365, [\chi])\).

Total New Old
Modular forms 536 440 96
Cusp forms 520 440 80
Eisenstein series 16 0 16

Trace form

\( 440 q - 440 q^{4} + 4 q^{6} + 216 q^{9} + O(q^{10}) \) \( 440 q - 440 q^{4} + 4 q^{6} + 216 q^{9} + 4 q^{14} + 432 q^{16} - 8 q^{19} + 28 q^{20} - 48 q^{21} - 68 q^{24} + 8 q^{25} + 16 q^{26} - 8 q^{29} + 60 q^{30} - 24 q^{31} - 20 q^{34} - 128 q^{36} + 32 q^{39} + 20 q^{40} + 16 q^{41} + 8 q^{44} - 20 q^{45} + 56 q^{46} + 232 q^{49} - 110 q^{50} - 48 q^{51} - 96 q^{54} - 48 q^{56} + 88 q^{59} - 12 q^{61} - 424 q^{64} - 36 q^{65} - 56 q^{69} - 28 q^{70} + 44 q^{71} + 4 q^{74} - 84 q^{75} + 48 q^{76} + 4 q^{79} - 82 q^{80} - 172 q^{81} + 12 q^{85} + 16 q^{86} - 92 q^{89} + 60 q^{90} - 16 q^{91} - 104 q^{94} - 14 q^{95} + 136 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2365, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2365, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2365, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(215, [\chi])\)\(^{\oplus 2}\)