Properties

Label 2366.2.g
Level $2366$
Weight $2$
Character orbit 2366.g
Rep. character $\chi_{2366}(1205,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $156$
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.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
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 784 156 628
Cusp forms 672 156 516
Eisenstein series 112 0 112

Trace form

\( 156 q - 2 q^{2} - 78 q^{4} - 4 q^{5} + 4 q^{8} - 78 q^{9} + O(q^{10}) \) \( 156 q - 2 q^{2} - 78 q^{4} - 4 q^{5} + 4 q^{8} - 78 q^{9} + 6 q^{10} - 4 q^{11} + 8 q^{14} + 4 q^{15} - 78 q^{16} + 6 q^{17} + 12 q^{18} - 16 q^{19} + 2 q^{20} - 8 q^{21} - 4 q^{22} + 4 q^{23} + 152 q^{25} - 24 q^{27} + 2 q^{29} + 8 q^{30} - 8 q^{31} - 2 q^{32} + 32 q^{33} + 12 q^{34} - 12 q^{35} - 78 q^{36} + 6 q^{37} - 32 q^{38} - 12 q^{40} + 14 q^{41} - 4 q^{42} + 8 q^{44} - 26 q^{45} + 12 q^{46} + 16 q^{47} - 78 q^{49} - 4 q^{50} - 56 q^{51} + 28 q^{53} - 12 q^{54} + 12 q^{55} - 4 q^{56} + 24 q^{57} + 2 q^{58} + 16 q^{59} - 8 q^{60} + 18 q^{61} + 12 q^{62} + 4 q^{63} + 156 q^{64} + 48 q^{66} + 12 q^{67} + 6 q^{68} - 20 q^{69} - 6 q^{72} + 36 q^{73} - 46 q^{74} + 40 q^{75} - 16 q^{76} - 16 q^{79} + 2 q^{80} - 130 q^{81} + 2 q^{82} + 24 q^{83} + 4 q^{84} + 34 q^{85} - 24 q^{86} - 28 q^{87} - 4 q^{88} - 28 q^{89} - 20 q^{90} - 8 q^{92} + 40 q^{93} - 8 q^{94} - 12 q^{95} - 12 q^{97} - 2 q^{98} - 40 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)