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Properties

Label 2365.2.do
Level $2365$
Weight $2$
Character orbit 2365.do
Rep. character $\chi_{2365}(13,\cdot)$
Character field $\Q(\zeta_{420})$
Dimension $24960$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.do (of order \(420\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2365 \)
Character field: \(\Q(\zeta_{420})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 25728 25728 0
Cusp forms 24960 24960 0
Eisenstein series 768 768 0

Trace form

\( 24960 q - 100 q^{2} - 78 q^{3} - 70 q^{5} - 120 q^{6} - 70 q^{7} - 100 q^{8} + O(q^{10}) \) \( 24960 q - 100 q^{2} - 78 q^{3} - 70 q^{5} - 120 q^{6} - 70 q^{7} - 100 q^{8} - 160 q^{11} - 148 q^{12} - 130 q^{13} - 78 q^{15} - 1152 q^{16} - 140 q^{17} - 130 q^{18} - 62 q^{20} - 48 q^{22} - 192 q^{23} - 70 q^{25} - 140 q^{26} - 84 q^{27} - 130 q^{28} - 170 q^{30} - 140 q^{31} + 10 q^{33} - 100 q^{35} - 2920 q^{36} - 36 q^{37} - 322 q^{38} - 90 q^{40} - 200 q^{41} + 72 q^{42} - 200 q^{45} - 340 q^{46} - 108 q^{47} - 554 q^{48} - 20 q^{50} - 200 q^{51} - 330 q^{52} - 20 q^{53} - 138 q^{55} - 312 q^{56} - 130 q^{57} - 58 q^{58} - 194 q^{60} - 260 q^{61} - 210 q^{62} - 110 q^{63} - 52 q^{66} - 48 q^{67} + 170 q^{68} - 244 q^{70} - 140 q^{71} + 170 q^{72} - 130 q^{73} - 60 q^{75} - 178 q^{77} + 100 q^{80} + 332 q^{81} - 100 q^{82} - 130 q^{83} - 240 q^{85} + 16 q^{86} + 344 q^{88} - 280 q^{90} - 140 q^{91} - 212 q^{92} - 40 q^{93} + 90 q^{95} - 400 q^{96} - 420 q^{97} + O(q^{100}) \)

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.