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Properties

Label 2366.2.ch
Level $2366$
Weight $2$
Character orbit 2366.ch
Rep. character $\chi_{2366}(33,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $5856$
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.ch (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 17664 5856 11808
Cusp forms 17280 5856 11424
Eisenstein series 384 0 384

Trace form

\( 5856 q + 8 q^{7} + 496 q^{9} + O(q^{10}) \) \( 5856 q + 8 q^{7} + 496 q^{9} + 12 q^{11} + 4 q^{12} + 16 q^{15} - 244 q^{16} + 8 q^{18} - 16 q^{19} - 24 q^{21} - 8 q^{28} + 8 q^{29} - 104 q^{30} - 16 q^{31} + 24 q^{33} + 32 q^{35} + 24 q^{36} - 40 q^{37} - 116 q^{39} - 24 q^{41} - 12 q^{42} + 72 q^{43} - 12 q^{46} - 36 q^{47} + 28 q^{49} - 24 q^{51} + 16 q^{52} + 8 q^{53} + 36 q^{55} + 12 q^{56} + 12 q^{57} + 32 q^{58} - 16 q^{60} - 36 q^{62} + 504 q^{63} + 52 q^{65} + 432 q^{67} + 84 q^{69} - 328 q^{70} - 28 q^{71} + 16 q^{72} + 76 q^{73} - 396 q^{74} + 752 q^{75} + 32 q^{76} - 8 q^{78} + 24 q^{79} - 504 q^{81} - 96 q^{82} - 108 q^{83} - 32 q^{84} - 264 q^{85} - 280 q^{86} - 24 q^{87} - 48 q^{89} - 44 q^{91} - 16 q^{92} - 48 q^{93} - 24 q^{95} - 380 q^{97} + 8 q^{98} - 28 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)