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Properties

Label 2365.2.cz
Level $2365$
Weight $2$
Character orbit 2365.cz
Rep. character $\chi_{2365}(12,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $5280$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.cz (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 215 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 6432 5280 1152
Cusp forms 6240 5280 960
Eisenstein series 192 0 192

Trace form

\( 5280 q - 8 q^{6} + O(q^{10}) \) \( 5280 q - 8 q^{6} + 920 q^{16} + 84 q^{18} - 32 q^{21} - 8 q^{23} - 88 q^{30} - 64 q^{31} + 280 q^{32} + 96 q^{35} - 2664 q^{36} - 180 q^{38} + 40 q^{40} + 64 q^{41} + 104 q^{43} - 40 q^{47} + 84 q^{48} + 112 q^{51} + 4 q^{52} - 104 q^{53} + 72 q^{56} - 20 q^{57} + 280 q^{60} - 72 q^{61} - 108 q^{62} - 104 q^{68} + 280 q^{70} + 24 q^{71} - 608 q^{72} - 32 q^{73} + 288 q^{76} - 24 q^{78} - 60 q^{80} + 48 q^{81} - 280 q^{82} - 28 q^{83} + 248 q^{86} - 664 q^{87} + 16 q^{90} - 160 q^{92} + 144 q^{93} + 216 q^{95} + 128 q^{96} + 192 q^{98} + O(q^{100}) \)

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

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