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Properties

Label 2365.2.br
Level $2365$
Weight $2$
Character orbit 2365.br
Rep. character $\chi_{2365}(173,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2016$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.br (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 2144 2016 128
Cusp forms 2080 2016 64
Eisenstein series 64 0 64

Trace form

\( 2016 q - 4 q^{3} + O(q^{10}) \) \( 2016 q - 4 q^{3} + 16 q^{11} - 64 q^{12} - 40 q^{15} + 504 q^{16} - 76 q^{20} - 28 q^{22} - 16 q^{23} - 36 q^{25} - 48 q^{26} - 4 q^{27} - 120 q^{28} - 24 q^{33} + 344 q^{36} + 4 q^{37} - 120 q^{41} - 40 q^{42} - 16 q^{45} + 20 q^{47} + 40 q^{48} - 80 q^{51} + 40 q^{53} + 84 q^{55} + 8 q^{56} - 80 q^{57} + 48 q^{58} - 136 q^{60} + 80 q^{61} - 300 q^{62} + 44 q^{66} - 80 q^{67} - 40 q^{70} - 104 q^{71} - 300 q^{72} - 120 q^{73} - 80 q^{75} - 164 q^{77} - 112 q^{78} - 120 q^{80} + 392 q^{81} - 32 q^{82} - 200 q^{83} - 80 q^{85} - 108 q^{88} - 160 q^{90} - 96 q^{91} + 196 q^{92} - 108 q^{93} - 180 q^{96} - 68 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2365, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)