Properties

Label 3549.2.br
Level $3549$
Weight $2$
Character orbit 3549.br
Rep. character $\chi_{3549}(530,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $782$
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.br (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

\( 782q + 3q^{3} + 748q^{4} + 2q^{7} - 3q^{9} + O(q^{10}) \) \( 782q + 3q^{3} + 748q^{4} + 2q^{7} - 3q^{9} + 6q^{10} + 12q^{12} + 9q^{15} + 680q^{16} + 36q^{18} - q^{19} + 9q^{21} + 18q^{22} + 12q^{24} + 317q^{25} - 10q^{28} + 4q^{30} - 29q^{31} + 15q^{33} + 24q^{34} + 20q^{36} - 18q^{40} - 43q^{42} + 4q^{43} + 6q^{45} - 66q^{48} - 8q^{49} + 8q^{51} - 18q^{54} - 54q^{55} - 30q^{58} + 9q^{60} - 33q^{61} + 556q^{64} - 57q^{66} - 27q^{67} + 39q^{69} + 84q^{70} + 123q^{72} + 22q^{73} - 16q^{76} - 19q^{79} + q^{81} - 78q^{82} - 21q^{84} + 30q^{85} + 30q^{88} - 84q^{94} + 24q^{96} - 7q^{97} + O(q^{100}) \)

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

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