↑

Properties

Label 2365.2.i
Level $2365$
Weight $2$
Character orbit 2365.i
Rep. character $\chi_{2365}(221,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $296$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 536 296 240
Cusp forms 520 296 224
Eisenstein series 16 0 16

Trace form

\( 296 q + 4 q^{3} + 304 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 156 q^{9} + O(q^{10}) \) \( 296 q + 4 q^{3} + 304 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 156 q^{9} + 8 q^{12} - 16 q^{13} + 4 q^{14} + 328 q^{16} + 4 q^{19} + 8 q^{20} + 56 q^{21} - 8 q^{22} + 8 q^{23} - 12 q^{24} - 148 q^{25} + 16 q^{26} - 32 q^{27} + 24 q^{28} - 16 q^{29} - 4 q^{30} - 16 q^{31} + 8 q^{33} - 12 q^{34} + 8 q^{35} - 180 q^{36} + 12 q^{37} - 12 q^{38} - 8 q^{39} - 16 q^{41} - 16 q^{42} - 60 q^{43} + 8 q^{44} + 16 q^{45} - 8 q^{47} + 16 q^{48} - 164 q^{49} - 48 q^{51} - 40 q^{52} - 12 q^{53} + 8 q^{54} + 8 q^{55} + 68 q^{56} + 48 q^{57} + 16 q^{58} + 24 q^{59} + 36 q^{61} - 60 q^{62} + 8 q^{63} + 416 q^{64} + 8 q^{65} + 4 q^{67} - 52 q^{68} - 32 q^{69} - 80 q^{70} + 4 q^{71} - 56 q^{72} - 4 q^{73} + 136 q^{74} - 8 q^{75} - 44 q^{76} + 16 q^{77} + 80 q^{78} - 16 q^{79} + 4 q^{80} - 196 q^{81} - 16 q^{82} - 36 q^{83} + 96 q^{84} + 8 q^{85} - 28 q^{86} + 32 q^{87} - 24 q^{88} + 4 q^{89} - 144 q^{90} - 68 q^{91} - 56 q^{92} - 12 q^{93} - 8 q^{94} - 16 q^{95} - 132 q^{96} - 120 q^{97} - 112 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2365, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(473, [\chi])\)\(^{\oplus 2}\)