Properties

Label 3549.2.j
Level $3549$
Weight $2$
Character orbit 3549.j
Rep. character $\chi_{3549}(991,\cdot)$
Character field $\Q(\zeta_{3})$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 410q - 6q^{3} - 204q^{4} + 3q^{7} + 410q^{9} + O(q^{10}) \) \( 410q - 6q^{3} - 204q^{4} + 3q^{7} + 410q^{9} - 16q^{10} - 8q^{11} + 8q^{12} + 20q^{14} - 194q^{16} - 8q^{17} - 6q^{19} + 8q^{20} + 5q^{21} - 2q^{22} + 8q^{23} + 24q^{24} - 195q^{25} - 6q^{27} - 8q^{28} + 11q^{31} - 20q^{32} + 56q^{34} + 2q^{35} - 204q^{36} - 23q^{37} - 28q^{38} + 34q^{40} - 18q^{41} + 2q^{42} + 20q^{44} + 8q^{46} - 12q^{47} + 18q^{48} - 7q^{49} + 2q^{50} - 12q^{51} - 32q^{53} + 30q^{55} - 58q^{56} + 38q^{57} + 40q^{58} + 32q^{59} - 32q^{60} - 10q^{61} - 8q^{62} + 3q^{63} + 412q^{64} + 16q^{66} + 34q^{67} - 44q^{68} + 8q^{69} - 76q^{70} - 10q^{71} - 4q^{73} - 12q^{74} + 29q^{75} + 12q^{76} + 26q^{77} + 19q^{79} + 40q^{80} + 410q^{81} - 28q^{82} - 64q^{83} - 22q^{84} + 20q^{85} - 20q^{86} + 30q^{87} + 48q^{88} - 16q^{89} - 16q^{90} - 28q^{92} + 17q^{93} - 120q^{94} + 56q^{95} - 14q^{96} - 23q^{97} + 82q^{98} - 8q^{99} + O(q^{100}) \)

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

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