Properties

Label 2365.2.bd
Level $2365$
Weight $2$
Character orbit 2365.bd
Rep. character $\chi_{2365}(738,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $880$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 215 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 1072 880 192
Cusp forms 1040 880 160
Eisenstein series 32 0 32

Trace form

\( 880 q + 8 q^{6} + O(q^{10}) \) \( 880 q + 8 q^{6} - 864 q^{16} - 84 q^{18} + 32 q^{21} + 8 q^{23} - 192 q^{30} - 48 q^{31} - 96 q^{35} - 416 q^{36} - 44 q^{38} - 40 q^{40} - 64 q^{41} + 8 q^{43} + 40 q^{47} - 84 q^{48} - 4 q^{52} - 8 q^{53} - 72 q^{56} + 20 q^{57} + 72 q^{61} + 108 q^{62} + 104 q^{68} - 24 q^{71} + 48 q^{72} + 144 q^{73} - 288 q^{76} + 24 q^{78} + 60 q^{80} + 344 q^{81} + 28 q^{83} - 24 q^{86} + 104 q^{87} - 16 q^{90} + 20 q^{92} - 144 q^{93} + 8 q^{95} - 128 q^{96} - 192 q^{98} + O(q^{100}) \)

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

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