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

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

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

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)