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Properties

Label 3229.2.c
Level $3229$
Weight $2$
Character orbit 3229.c
Rep. character $\chi_{3229}(914,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $536$
Sturm bound $538$

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Defining parameters

Level: \( N \) \(=\) \( 3229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3229.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3229 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(538\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3229, [\chi])\).

Total New Old
Modular forms 540 540 0
Cusp forms 536 536 0
Eisenstein series 4 4 0

Trace form

\( 536 q - 4 q^{2} + 536 q^{4} - 16 q^{5} - 10 q^{6} + 2 q^{7} - 24 q^{8} - 264 q^{9} + O(q^{10}) \) \( 536 q - 4 q^{2} + 536 q^{4} - 16 q^{5} - 10 q^{6} + 2 q^{7} - 24 q^{8} - 264 q^{9} - 14 q^{10} - 7 q^{12} + 2 q^{15} + 544 q^{16} - 2 q^{17} + 5 q^{18} - 8 q^{19} - 54 q^{20} - 22 q^{21} + 4 q^{22} - 12 q^{23} - 22 q^{24} + 488 q^{25} - 32 q^{26} + 30 q^{27} + 9 q^{28} + 2 q^{29} + q^{30} + 8 q^{31} - 52 q^{32} + 6 q^{33} - 20 q^{34} - 12 q^{35} - 258 q^{36} - 8 q^{37} + 10 q^{38} + 4 q^{39} - 196 q^{40} + 13 q^{41} + 40 q^{42} + 10 q^{43} + 50 q^{44} + 20 q^{45} - 42 q^{46} + 10 q^{47} + 14 q^{48} - 258 q^{49} - 76 q^{50} - q^{51} + 38 q^{52} - 22 q^{53} - 2 q^{54} + 5 q^{55} - 34 q^{56} + 50 q^{57} + 48 q^{58} + 11 q^{59} - 14 q^{60} + 44 q^{61} - 102 q^{62} + 27 q^{63} + 528 q^{64} + 52 q^{65} - 36 q^{66} + 32 q^{67} + 35 q^{68} + 6 q^{69} - 52 q^{70} + 22 q^{71} - 11 q^{72} + 24 q^{73} - 29 q^{74} - 23 q^{75} - 22 q^{76} + 90 q^{77} - 22 q^{78} - 10 q^{79} - 30 q^{80} - 260 q^{81} + 38 q^{82} + 27 q^{83} - 100 q^{84} - 28 q^{85} - 36 q^{86} + 16 q^{87} + 22 q^{88} - 17 q^{89} - 23 q^{90} - 37 q^{91} - 4 q^{92} - 27 q^{93} + 28 q^{94} - 55 q^{96} + 14 q^{97} + 77 q^{98} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3229, [\chi])\) into newform subspaces

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