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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 $970$

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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

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

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

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