↑

Properties

Label 2365.2.m
Level $2365$
Weight $2$
Character orbit 2365.m
Rep. character $\chi_{2365}(1332,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $440$
Sturm bound $528$

Related objects

Downloads

Learn more

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

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

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

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