Properties

Label 2365.2.m
Level 2365
Weight 2
Character orbit m
Rep. character \(\chi_{2365}(1332,\cdot)\)
Character field \(\Q(\zeta_{4})\)
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 215 \)
Character field: \(\Q(i)\)
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

\( 440q + 16q^{6} + O(q^{10}) \) \( 440q + 16q^{6} - 456q^{16} - 32q^{21} + 16q^{23} + 48q^{31} - 48q^{35} + 488q^{36} - 88q^{38} - 80q^{40} - 32q^{41} - 8q^{43} - 40q^{47} - 8q^{52} - 16q^{53} + 40q^{57} - 104q^{68} + 168q^{78} - 632q^{81} + 56q^{83} + 72q^{86} + 112q^{87} - 8q^{90} - 176q^{92} - 104q^{95} - 256q^{96} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database