Properties

Label 3549.2.em
Level $3549$
Weight $2$
Character orbit 3549.em
Rep. character $\chi_{3549}(2,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $23088$
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.em (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3549 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 23472 23472 0
Cusp forms 23088 23088 0
Eisenstein series 384 384 0

Trace form

\( 23088q - 28q^{3} - 52q^{4} - 100q^{6} - 96q^{7} - 28q^{9} + O(q^{10}) \) \( 23088q - 28q^{3} - 52q^{4} - 100q^{6} - 96q^{7} - 28q^{9} - 40q^{10} - 62q^{12} - 192q^{13} - 98q^{15} + 1820q^{16} - 24q^{18} - 32q^{19} - 46q^{21} - 96q^{22} - 28q^{24} - 52q^{25} - 88q^{27} - 172q^{28} + 164q^{30} - 94q^{31} - 10q^{33} - 160q^{34} - 44q^{36} - 66q^{37} + 172q^{39} - 96q^{40} - 62q^{42} - 100q^{43} - 24q^{45} - 444q^{46} - 80q^{48} - 48q^{49} + 10q^{51} - 92q^{52} - 40q^{54} - 200q^{55} - 114q^{57} - 96q^{58} + 32q^{60} - 56q^{61} - 202q^{63} - 208q^{64} - 90q^{66} - 208q^{67} - 128q^{69} + 208q^{70} - 72q^{72} + 30q^{73} - 286q^{75} - 324q^{76} - 186q^{78} - 20q^{79} - 16q^{81} - 88q^{82} - 224q^{84} - 264q^{85} + 34q^{87} - 392q^{88} - 104q^{90} - 128q^{91} - 72q^{93} + 276q^{94} + 64q^{96} - 270q^{97} - 94q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3549, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.