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Properties

Label 2365.2.n
Level $2365$
Weight $2$
Character orbit 2365.n
Rep. character $\chi_{2365}(861,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $672$
Sturm bound $528$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 1072 672 400
Cusp forms 1040 672 368
Eisenstein series 32 0 32

Trace form

\( 672 q - 168 q^{4} - 180 q^{9} + O(q^{10}) \) \( 672 q - 168 q^{4} - 180 q^{9} - 16 q^{10} + 2 q^{13} + 4 q^{14} - 12 q^{15} - 168 q^{16} - 4 q^{17} + 32 q^{18} + 8 q^{19} + 64 q^{21} - 88 q^{22} + 28 q^{23} - 40 q^{24} - 168 q^{25} - 8 q^{26} - 12 q^{27} + 48 q^{28} - 52 q^{29} + 32 q^{30} + 4 q^{31} + 40 q^{32} + 40 q^{33} + 88 q^{34} + 24 q^{35} - 144 q^{36} - 4 q^{38} - 76 q^{39} + 12 q^{40} - 68 q^{41} - 92 q^{42} - 32 q^{43} + 116 q^{44} + 72 q^{46} + 8 q^{47} - 28 q^{48} - 164 q^{49} - 40 q^{51} + 92 q^{52} + 12 q^{53} - 12 q^{54} + 8 q^{55} - 60 q^{56} + 40 q^{57} - 64 q^{58} + 32 q^{59} - 10 q^{60} - 24 q^{61} + 104 q^{62} - 36 q^{63} - 192 q^{64} + 32 q^{65} + 118 q^{66} - 28 q^{67} - 8 q^{68} + 136 q^{69} - 72 q^{70} + 56 q^{71} - 56 q^{72} - 84 q^{73} - 94 q^{74} - 184 q^{76} - 64 q^{77} - 112 q^{78} + 20 q^{79} - 48 q^{80} - 204 q^{81} + 32 q^{82} + 4 q^{83} + 68 q^{84} + 24 q^{85} - 96 q^{87} + 4 q^{88} + 16 q^{89} + 20 q^{90} - 112 q^{91} - 88 q^{92} + 92 q^{93} + 12 q^{94} + 32 q^{95} - 10 q^{96} - 6 q^{97} + 120 q^{98} + 154 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2365, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(473, [\chi])\)\(^{\oplus 2}\)