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Properties

Label 2365.2.bo
Level $2365$
Weight $2$
Character orbit 2365.bo
Rep. character $\chi_{2365}(36,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1408$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.bo (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 2144 1408 736
Cusp forms 2080 1408 672
Eisenstein series 64 0 64

Trace form

\( 1408 q + 8 q^{3} - 344 q^{4} - 12 q^{6} + 8 q^{7} - 64 q^{8} + 200 q^{9} + O(q^{10}) \) \( 1408 q + 8 q^{3} - 344 q^{4} - 12 q^{6} + 8 q^{7} - 64 q^{8} + 200 q^{9} + 4 q^{11} + 24 q^{12} - 6 q^{13} + 2 q^{14} - 328 q^{16} - 8 q^{17} + 30 q^{18} + 18 q^{19} - 4 q^{20} + 36 q^{22} - 36 q^{23} - 36 q^{24} + 176 q^{25} + 16 q^{26} + 56 q^{27} + 46 q^{28} - 16 q^{29} + 8 q^{30} + 4 q^{31} + 192 q^{32} + 6 q^{33} + 28 q^{34} + 72 q^{36} - 20 q^{37} - 8 q^{38} + 16 q^{39} + 48 q^{41} + 16 q^{42} + 28 q^{43} - 108 q^{44} + 58 q^{46} + 56 q^{47} + 56 q^{48} + 168 q^{49} - 36 q^{51} + 16 q^{52} - 44 q^{53} - 120 q^{54} - 32 q^{55} + 76 q^{56} - 30 q^{57} + 58 q^{58} + 12 q^{59} - 42 q^{60} - 8 q^{61} + 32 q^{62} - 76 q^{63} - 320 q^{64} + 128 q^{65} + 82 q^{66} - 48 q^{67} - 168 q^{68} - 116 q^{69} - 16 q^{70} + 48 q^{71} - 92 q^{72} - 4 q^{73} - 42 q^{74} + 24 q^{75} + 44 q^{76} - 2 q^{77} + 192 q^{78} + 88 q^{79} - 8 q^{80} + 92 q^{81} + 220 q^{82} - 8 q^{83} + 232 q^{84} - 16 q^{85} + 142 q^{86} - 88 q^{87} - 132 q^{88} - 152 q^{89} + 32 q^{90} + 24 q^{91} + 120 q^{92} - 2 q^{93} - 160 q^{94} - 158 q^{96} + 24 q^{97} - 176 q^{98} - 230 q^{99} + O(q^{100}) \)

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

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