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Properties

Label 2365.2.y
Level $2365$
Weight $2$
Character orbit 2365.y
Rep. character $\chi_{2365}(171,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $704$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.y (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 1072 704 368
Cusp forms 1040 704 336
Eisenstein series 32 0 32

Trace form

\( 704 q - 184 q^{4} + 20 q^{6} + 152 q^{9} + O(q^{10}) \) \( 704 q - 184 q^{4} + 20 q^{6} + 152 q^{9} - 4 q^{11} + 10 q^{13} + 20 q^{14} - 184 q^{16} + 44 q^{23} - 60 q^{24} + 176 q^{25} - 12 q^{31} + 300 q^{36} + 16 q^{38} + 60 q^{44} - 32 q^{47} - 160 q^{49} + 44 q^{53} - 84 q^{56} - 60 q^{57} + 52 q^{58} - 4 q^{59} - 42 q^{60} - 200 q^{64} - 242 q^{66} - 60 q^{67} + 260 q^{68} - 150 q^{74} + 88 q^{78} + 160 q^{79} - 340 q^{81} + 20 q^{83} - 240 q^{84} - 114 q^{86} - 176 q^{92} - 130 q^{96} + 210 q^{97} + 226 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2365, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(473, [\chi])\)\(^{\oplus 2}\)