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Properties

Label 2366.2.e
Level $2366$
Weight $2$
Character orbit 2366.e
Rep. character $\chi_{2366}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $204$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2366.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2366, [\chi])\).

Total New Old
Modular forms 784 204 580
Cusp forms 672 204 468
Eisenstein series 112 0 112

Trace form

\( 204 q + 2 q^{3} + 204 q^{4} + 6 q^{7} - 104 q^{9} + O(q^{10}) \) \( 204 q + 2 q^{3} + 204 q^{4} + 6 q^{7} - 104 q^{9} + 4 q^{10} + 10 q^{11} + 2 q^{12} + 2 q^{14} + 4 q^{15} + 204 q^{16} - 8 q^{17} + 6 q^{21} - 4 q^{22} - 8 q^{23} - 90 q^{25} + 8 q^{27} + 6 q^{28} - 16 q^{30} + 22 q^{31} - 16 q^{33} - 6 q^{35} - 104 q^{36} + 40 q^{37} + 8 q^{38} + 4 q^{40} + 2 q^{41} + 32 q^{42} - 4 q^{43} + 10 q^{44} + 40 q^{45} + 16 q^{46} - 6 q^{47} + 2 q^{48} + 32 q^{49} - 12 q^{50} - 28 q^{51} + 10 q^{53} - 12 q^{54} - 10 q^{55} + 2 q^{56} + 28 q^{57} - 16 q^{59} + 4 q^{60} + 38 q^{61} + 18 q^{62} - 66 q^{63} + 204 q^{64} + 16 q^{66} - 8 q^{68} + 18 q^{69} - 40 q^{70} + 26 q^{71} - 28 q^{73} + 68 q^{75} + 30 q^{77} + 6 q^{79} - 150 q^{81} + 16 q^{82} - 84 q^{83} + 6 q^{84} - 20 q^{85} - 10 q^{86} - 144 q^{87} - 4 q^{88} - 28 q^{89} - 16 q^{90} - 8 q^{92} + 8 q^{93} + 30 q^{94} + 24 q^{95} - 34 q^{97} - 48 q^{98} - 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2366, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2366, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)