Properties

Label 3549.2.i
Level $3549$
Weight $2$
Character orbit 3549.i
Rep. character $\chi_{3549}(508,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $414$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
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 1028 414 614
Cusp forms 916 414 502
Eisenstein series 112 0 112

Trace form

\( 414q - 2q^{2} + q^{3} - 210q^{4} + 2q^{5} + 4q^{6} - 3q^{7} - 207q^{9} + O(q^{10}) \) \( 414q - 2q^{2} + q^{3} - 210q^{4} + 2q^{5} + 4q^{6} - 3q^{7} - 207q^{9} + 12q^{10} - 6q^{11} + 2q^{12} - 14q^{14} - 4q^{15} - 224q^{16} - 8q^{17} - 2q^{18} - 15q^{19} + 24q^{20} - 4q^{21} + 32q^{22} + 8q^{23} - 12q^{24} - 201q^{25} - 2q^{27} + 32q^{28} + 8q^{29} + 4q^{30} - 3q^{31} - 12q^{32} + 2q^{33} - 16q^{34} - 18q^{35} + 420q^{36} - 13q^{37} + 30q^{38} + 4q^{40} + 52q^{41} + 22q^{42} - 34q^{43} - 36q^{44} + 2q^{45} - 40q^{46} + 30q^{47} - 24q^{48} - 27q^{49} + 4q^{50} + 4q^{53} - 2q^{54} - 16q^{55} + 32q^{56} + 14q^{57} + 56q^{58} - 4q^{59} + 8q^{60} + 14q^{61} - 92q^{62} + 3q^{63} + 464q^{64} + 20q^{66} + 19q^{67} - 44q^{68} - 16q^{69} - 8q^{70} + 44q^{71} - 39q^{73} + 18q^{74} - q^{75} + 92q^{76} - 36q^{77} - 9q^{79} - 76q^{80} - 207q^{81} - 20q^{82} - 4q^{83} - 18q^{84} - 40q^{85} - 66q^{86} + 8q^{87} - 24q^{88} + 16q^{89} - 24q^{90} + 80q^{92} - 15q^{93} - 36q^{94} + 10q^{95} - 36q^{96} - 52q^{97} - 52q^{98} + 12q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)