Properties

Label 3549.2.cd
Level $3549$
Weight $2$
Character orbit 3549.cd
Rep. character $\chi_{3549}(746,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1560$
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.cd (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 2056 1720 336
Cusp forms 1832 1560 272
Eisenstein series 224 160 64

Trace form

\( 1560q + 4q^{3} + 16q^{6} + 2q^{7} + 4q^{9} + O(q^{10}) \) \( 1560q + 4q^{3} + 16q^{6} + 2q^{7} + 4q^{9} + 12q^{15} + 656q^{16} + 26q^{18} + 6q^{19} + 6q^{21} + 32q^{22} - 20q^{24} - 32q^{27} + 36q^{28} + 14q^{31} + 16q^{33} - 48q^{34} + 6q^{37} + 64q^{40} + 84q^{42} + 2q^{45} - 24q^{46} + 8q^{48} - 14q^{54} + 44q^{57} + 28q^{58} - 44q^{60} - 24q^{61} - 32q^{63} + 2q^{67} + 44q^{70} + 26q^{72} + 38q^{73} + 8q^{76} - 104q^{79} - 52q^{81} + 158q^{84} - 80q^{85} + 160q^{87} - 4q^{93} - 32q^{94} + 126q^{96} + 4q^{99} + O(q^{100}) \)

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

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