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Properties

Label 3549.2.bf
Level $3549$
Weight $2$
Character orbit 3549.bf
Rep. character $\chi_{3549}(698,\cdot)$
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.bf (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

\( 782 q + 370 q^{4} + 12 q^{6} + 9 q^{7} - 2 q^{9} + O(q^{10}) \) \( 782 q + 370 q^{4} + 12 q^{6} + 9 q^{7} - 2 q^{9} + 9 q^{15} - 332 q^{16} - 2 q^{18} - 7 q^{21} - 10 q^{22} - 309 q^{25} + 48 q^{28} - 20 q^{30} + 39 q^{31} - 16 q^{36} - 11 q^{37} - 162 q^{40} + 74 q^{42} + 12 q^{43} + 3 q^{45} + 90 q^{48} - 7 q^{49} + 16 q^{51} + 27 q^{54} - 6 q^{55} + 26 q^{57} + 60 q^{58} - 55 q^{60} + 59 q^{63} - 444 q^{64} - 141 q^{66} + 66 q^{67} + 33 q^{69} - 20 q^{70} + 34 q^{72} - 60 q^{73} + 6 q^{75} + 12 q^{76} - 61 q^{79} + 30 q^{81} - 12 q^{84} + 2 q^{85} - 111 q^{87} - 92 q^{88} - 13 q^{93} - 30 q^{96} - 33 q^{97} - 22 q^{99} + O(q^{100}) \)

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

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