Properties

Label 3549.2.t
Level $3549$
Weight $2$
Character orbit 3549.t
Rep. character $\chi_{3549}(823,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $410$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 1026 410 616
Cusp forms 914 410 504
Eisenstein series 112 0 112

Trace form

\( 410q - 3q^{3} - 408q^{4} - 4q^{7} - 205q^{9} + O(q^{10}) \) \( 410q - 3q^{3} - 408q^{4} - 4q^{7} - 205q^{9} + 8q^{10} + 12q^{11} + 8q^{12} + 28q^{14} + 420q^{16} - 16q^{17} - 3q^{19} + 24q^{20} + 7q^{21} - 14q^{22} + 16q^{23} + 195q^{25} + 6q^{27} - 8q^{28} + 3q^{31} + 2q^{35} + 204q^{36} - 12q^{38} - 14q^{40} - 18q^{41} - 26q^{42} - 8q^{43} - 12q^{44} - 36q^{47} - 18q^{48} - 6q^{49} + 102q^{50} + 4q^{51} - 34q^{55} - 6q^{56} + 12q^{58} - 36q^{60} - 21q^{61} + 32q^{62} + 5q^{63} - 428q^{64} - 16q^{66} + 33q^{67} + 8q^{68} + 24q^{69} - 36q^{70} - 18q^{71} + 42q^{73} + 24q^{74} - 26q^{75} - 74q^{77} - 19q^{79} - 48q^{80} - 205q^{81} - 6q^{82} - 28q^{84} + 48q^{85} - 36q^{86} + 36q^{87} + 24q^{88} - 16q^{90} - 172q^{92} - 56q^{94} + 80q^{95} + 30q^{96} - 27q^{97} - 102q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)