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Properties

Label 3549.2.bw
Level $3549$
Weight $2$
Character orbit 3549.bw
Rep. character $\chi_{3549}(695,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1564$
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.bw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(970\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3549, [\chi])\).

Total New Old
Modular forms 2052 1724 328
Cusp forms 1828 1564 264
Eisenstein series 224 160 64

Trace form

\( 1564 q + 4 q^{3} + 12 q^{4} + 4 q^{6} + 16 q^{7} + 4 q^{9} + O(q^{10}) \) \( 1564 q + 4 q^{3} + 12 q^{4} + 4 q^{6} + 16 q^{7} + 4 q^{9} + 36 q^{12} + 6 q^{15} + 664 q^{16} - 22 q^{18} + 14 q^{19} + 24 q^{21} + 8 q^{22} + 4 q^{24} - 32 q^{27} + 72 q^{28} + 12 q^{31} - 50 q^{33} + 48 q^{34} + 60 q^{36} - 8 q^{37} - 92 q^{40} - 96 q^{42} + 108 q^{43} - 58 q^{45} - 48 q^{46} + 32 q^{48} - 2 q^{49} - 36 q^{51} + 22 q^{54} + 24 q^{55} - 10 q^{57} + 28 q^{58} + 4 q^{60} + 72 q^{61} - 20 q^{63} + 30 q^{66} - 74 q^{67} + 54 q^{69} - 64 q^{70} + 98 q^{72} - 62 q^{73} + 42 q^{75} - 116 q^{76} - 32 q^{79} + 44 q^{81} - 4 q^{84} - 56 q^{85} + 106 q^{87} - 16 q^{93} - 32 q^{94} + 54 q^{96} - 62 q^{97} + 10 q^{99} + O(q^{100}) \)

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

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