Properties

Label 3549.2.y
Level $3549$
Weight $2$
Character orbit 3549.y
Rep. character $\chi_{3549}(992,\cdot)$
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.y (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

\( 782q - 374q^{4} + 7q^{7} + 6q^{9} + O(q^{10}) \) \( 782q - 374q^{4} + 7q^{7} + 6q^{9} + 12q^{12} + 9q^{15} - 340q^{16} - 36q^{18} - 2q^{19} - 9q^{21} + 18q^{22} + 24q^{24} + 317q^{25} - 8q^{28} - 8q^{30} + 29q^{31} + 30q^{33} - 24q^{34} + 20q^{36} + 27q^{37} - 18q^{40} + 50q^{42} + 4q^{43} + 3q^{45} + 24q^{46} + 66q^{48} - 23q^{49} + 8q^{51} - 9q^{54} + 54q^{55} - 9q^{60} + 9q^{63} + 556q^{64} - 57q^{66} - 39q^{69} - 84q^{70} - 22q^{73} - 60q^{75} + 16q^{76} - 19q^{79} - 2q^{81} - 12q^{84} + 30q^{85} - 111q^{87} - 60q^{88} - 3q^{93} - 24q^{96} + 7q^{97} + O(q^{100}) \)

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

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