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Properties

Label 3549.2.bv
Level $3549$
Weight $2$
Character orbit 3549.bv
Rep. character $\chi_{3549}(1094,\cdot)$
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.bv (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

\( 1564 q - 2 q^{3} + 4 q^{6} + 8 q^{7} - 2 q^{9} + O(q^{10}) \) \( 1564 q - 2 q^{3} + 4 q^{6} + 8 q^{7} - 2 q^{9} + 12 q^{10} - 36 q^{12} + 6 q^{15} - 1328 q^{16} + 2 q^{18} + 20 q^{19} + 6 q^{21} + 8 q^{22} - 2 q^{24} - 32 q^{27} - 68 q^{28} - 18 q^{30} - 42 q^{31} + 16 q^{33} + 48 q^{34} + 60 q^{36} - 14 q^{37} - 92 q^{40} + 6 q^{42} + 108 q^{43} + 2 q^{45} + 24 q^{46} + 32 q^{48} + 56 q^{49} + 36 q^{51} - 14 q^{54} + 24 q^{55} - 10 q^{57} - 44 q^{58} + 58 q^{60} - 36 q^{61} - 20 q^{63} + 30 q^{66} + 52 q^{67} + 54 q^{69} + 104 q^{70} - 46 q^{72} + 82 q^{73} - 116 q^{76} - 32 q^{79} - 22 q^{81} - 36 q^{82} - 172 q^{84} - 56 q^{85} - 212 q^{87} - 132 q^{88} - 46 q^{93} + 16 q^{94} + 90 q^{96} - 62 q^{97} + 10 q^{99} + O(q^{100}) \)

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

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