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Properties

Label 2365.2.bn
Level $2365$
Weight $2$
Character orbit 2365.bn
Rep. character $\chi_{2365}(914,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1320$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.bn (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 215 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 1608 1320 288
Cusp forms 1560 1320 240
Eisenstein series 48 0 48

Trace form

\( 1320 q + 220 q^{4} - 8 q^{6} + 200 q^{9} + O(q^{10}) \) \( 1320 q + 220 q^{4} - 8 q^{6} + 200 q^{9} - 12 q^{14} - 200 q^{16} + 16 q^{19} + 28 q^{20} - 48 q^{21} - 32 q^{24} - 20 q^{25} + 16 q^{26} + 72 q^{29} + 104 q^{30} + 32 q^{31} - 8 q^{34} - 28 q^{35} + 1376 q^{36} - 24 q^{39} - 40 q^{40} - 32 q^{41} + 8 q^{44} - 20 q^{45} + 56 q^{46} - 1272 q^{49} - 120 q^{50} + 128 q^{51} - 72 q^{54} + 24 q^{56} + 16 q^{59} + 140 q^{60} - 48 q^{61} + 236 q^{64} - 12 q^{65} - 12 q^{69} + 112 q^{70} + 8 q^{71} - 64 q^{74} - 140 q^{75} - 96 q^{76} - 72 q^{79} - 112 q^{80} - 120 q^{81} - 36 q^{84} + 60 q^{85} + 104 q^{86} - 36 q^{89} - 14 q^{90} - 64 q^{91} - 120 q^{94} + 80 q^{95} - 328 q^{96} + O(q^{100}) \)

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

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