Properties

Label 3549.2.r
Level $3549$
Weight $2$
Character orbit 3549.r
Rep. character $\chi_{3549}(1160,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $782$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 1026 862 164
Cusp forms 914 782 132
Eisenstein series 112 80 32

Trace form

\( 782q + 3q^{3} - 740q^{4} - 12q^{6} + 6q^{7} + q^{9} + O(q^{10}) \) \( 782q + 3q^{3} - 740q^{4} - 12q^{6} + 6q^{7} + q^{9} + 6q^{10} + 9q^{15} + 664q^{16} - 2q^{18} + 21q^{19} - 7q^{21} - 10q^{22} + 18q^{24} - 309q^{25} + 6q^{28} + 10q^{30} + 39q^{31} + 45q^{33} - 16q^{36} + 22q^{37} - 162q^{40} - 7q^{42} + 12q^{43} - 90q^{48} + 8q^{49} + 16q^{51} + 6q^{55} + 26q^{57} - 30q^{58} - 55q^{60} + 45q^{61} - 28q^{63} - 444q^{64} - 141q^{66} - 33q^{67} - 33q^{69} - 20q^{70} - 17q^{72} - 60q^{73} - 12q^{76} - 61q^{79} - 15q^{81} + 162q^{82} + 141q^{84} + 2q^{85} + 46q^{88} + 26q^{93} - 36q^{94} - 30q^{96} + 33q^{97} - 22q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)