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

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

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

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