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Properties

Label 3549.2.n
Level $3549$
Weight $2$
Character orbit 3549.n
Rep. character $\chi_{3549}(239,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $616$
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.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(i)\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 1024 616 408
Cusp forms 912 616 296
Eisenstein series 112 0 112

Trace form

\( 616 q - 12 q^{6} + O(q^{10}) \) \( 616 q - 12 q^{6} + 4 q^{15} - 648 q^{16} + 20 q^{18} - 8 q^{19} - 4 q^{21} - 32 q^{22} + 8 q^{24} + 24 q^{27} + 16 q^{31} - 36 q^{33} + 48 q^{37} - 32 q^{40} - 28 q^{45} + 24 q^{46} - 48 q^{48} - 36 q^{54} + 128 q^{55} + 32 q^{57} - 24 q^{58} - 44 q^{60} + 96 q^{61} - 8 q^{63} + 168 q^{66} - 40 q^{67} - 24 q^{70} - 32 q^{72} - 16 q^{73} - 104 q^{76} - 48 q^{79} - 88 q^{81} - 12 q^{84} + 32 q^{85} + 48 q^{87} + 20 q^{93} - 192 q^{94} - 8 q^{96} + 96 q^{97} + 12 q^{99} + O(q^{100}) \)

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

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