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Properties

Label 3549.2.cq
Level $3549$
Weight $2$
Character orbit 3549.cq
Rep. character $\chi_{3549}(16,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $5832$
Sturm bound $970$

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Defining parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.cq (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(970\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3549, [\chi])\).

Total New Old
Modular forms 11736 5832 5904
Cusp forms 11544 5832 5712
Eisenstein series 192 0 192

Trace form

\( 5832 q + 3 q^{3} - 488 q^{4} + 243 q^{9} + O(q^{10}) \) \( 5832 q + 3 q^{3} - 488 q^{4} + 243 q^{9} + 8 q^{10} + 4 q^{11} + 8 q^{12} + 24 q^{13} + 12 q^{14} - 508 q^{16} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 6 q^{22} - 12 q^{24} + 245 q^{25} - 46 q^{26} - 6 q^{27} + 16 q^{28} + 11 q^{31} - 220 q^{32} + 56 q^{34} - 10 q^{35} + 244 q^{36} + 46 q^{37} - 280 q^{38} - 13 q^{39} + 34 q^{40} - 18 q^{41} - 116 q^{42} - 8 q^{43} + 20 q^{44} - 16 q^{46} - 12 q^{47} + 18 q^{48} - 170 q^{49} + 2 q^{50} - 4 q^{51} + 66 q^{52} - 224 q^{53} + 38 q^{55} + 62 q^{56} + 38 q^{57} - 72 q^{58} + 144 q^{59} - 32 q^{60} + 13 q^{61} - 24 q^{62} - 3 q^{63} - 484 q^{64} + 30 q^{65} + 16 q^{66} + 191 q^{67} - 220 q^{68} + 16 q^{69} + 28 q^{70} - 166 q^{71} - 4 q^{73} - 184 q^{74} - 58 q^{75} + 168 q^{76} - 6 q^{77} - 10 q^{78} + 19 q^{79} - 20 q^{80} + 243 q^{81} + 14 q^{82} - 64 q^{83} + 8 q^{84} - 188 q^{85} + 136 q^{86} - 60 q^{87} + 32 q^{89} - 16 q^{90} - 108 q^{91} + 36 q^{92} + 187 q^{93} - 88 q^{94} - 136 q^{95} - 14 q^{96} + 133 q^{97} + 58 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3549, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3549, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)