↑

Properties

Label 3549.2.cs
Level $3549$
Weight $2$
Character orbit 3549.cs
Rep. character $\chi_{3549}(100,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $5832$
Sturm bound $970$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.cs (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

\( 5832 q - 6 q^{3} + 244 q^{4} + 3 q^{7} - 486 q^{9} + O(q^{10}) \) \( 5832 q - 6 q^{3} + 244 q^{4} + 3 q^{7} - 486 q^{9} - 16 q^{10} - 8 q^{11} + 8 q^{12} + 24 q^{13} + 12 q^{14} + 254 q^{16} - 6 q^{19} + 8 q^{20} + 5 q^{21} + 6 q^{22} + 24 q^{24} + 245 q^{25} + 2 q^{26} - 6 q^{27} - 8 q^{28} + 11 q^{31} + 110 q^{32} + 56 q^{34} + 2 q^{35} + 244 q^{36} - 23 q^{37} + 500 q^{38} + 8 q^{39} + 34 q^{40} - 18 q^{41} - 128 q^{42} - 8 q^{43} + 20 q^{44} + 8 q^{46} - 12 q^{47} + 18 q^{48} - 155 q^{49} + 2 q^{50} - 4 q^{51} - 48 q^{52} + 400 q^{53} + 38 q^{55} - 10 q^{56} + 38 q^{57} + 144 q^{58} + 240 q^{59} - 32 q^{60} - 26 q^{61} - 24 q^{62} + 3 q^{63} - 484 q^{64} + 48 q^{65} + 16 q^{66} - 226 q^{67} + 110 q^{68} + 16 q^{69} + 28 q^{70} - 166 q^{71} - 4 q^{73} + 404 q^{74} + 29 q^{75} + 168 q^{76} - 6 q^{77} - 10 q^{78} + 19 q^{79} + 40 q^{80} - 486 q^{81} - 28 q^{82} - 64 q^{83} - 22 q^{84} - 188 q^{85} - 332 q^{86} + 30 q^{87} - 16 q^{89} - 16 q^{90} - 117 q^{91} + 36 q^{92} - 113 q^{93} - 58 q^{94} - 88 q^{95} - 14 q^{96} + 133 q^{97} + 82 q^{98} - 8 q^{99} + O(q^{100}) \)

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

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