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Properties

Label 2366.2.f
Level $2366$
Weight $2$
Character orbit 2366.f
Rep. character $\chi_{2366}(1353,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $208$
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.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
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 784 208 576
Cusp forms 672 208 464
Eisenstein series 112 0 112

Trace form

\( 208 q - 104 q^{4} - 8 q^{7} - 100 q^{9} + O(q^{10}) \) \( 208 q - 104 q^{4} - 8 q^{7} - 100 q^{9} + 4 q^{10} + 4 q^{11} + 8 q^{14} - 32 q^{15} - 104 q^{16} + 4 q^{17} - 4 q^{19} + 16 q^{21} + 8 q^{22} + 16 q^{23} - 104 q^{25} + 24 q^{27} + 4 q^{28} - 24 q^{29} - 4 q^{30} + 12 q^{31} - 28 q^{33} - 24 q^{35} + 200 q^{36} + 8 q^{38} + 4 q^{40} + 32 q^{41} - 4 q^{42} - 56 q^{43} + 4 q^{44} + 40 q^{45} + 4 q^{46} + 12 q^{47} - 36 q^{49} - 48 q^{50} - 4 q^{51} - 8 q^{53} - 12 q^{54} + 56 q^{55} - 4 q^{56} - 48 q^{57} + 24 q^{58} + 8 q^{59} + 16 q^{60} + 16 q^{61} + 4 q^{63} + 208 q^{64} + 16 q^{66} + 8 q^{67} + 4 q^{68} + 72 q^{69} + 8 q^{70} + 8 q^{71} + 4 q^{73} + 12 q^{75} + 8 q^{76} - 12 q^{77} + 20 q^{79} - 104 q^{81} - 8 q^{82} + 24 q^{83} - 32 q^{84} - 32 q^{85} - 4 q^{86} + 48 q^{87} - 4 q^{88} - 28 q^{89} - 16 q^{90} - 32 q^{92} - 20 q^{93} - 24 q^{94} - 24 q^{95} - 32 q^{97} + 24 q^{98} - 40 q^{99} + O(q^{100}) \)

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

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