Properties

Label 3549.2.cg
Level $3549$
Weight $2$
Character orbit 3549.cg
Rep. character $\chi_{3549}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $820$
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.cg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 2052 820 1232
Cusp forms 1828 820 1008
Eisenstein series 224 0 224

Trace form

\( 820q + 4q^{7} - 820q^{9} + O(q^{10}) \) \( 820q + 4q^{7} - 820q^{9} - 8q^{11} + 8q^{12} - 16q^{14} + 404q^{16} + 10q^{19} - 2q^{21} - 16q^{22} - 4q^{28} - 32q^{29} - 8q^{31} - 20q^{32} - 16q^{35} - 16q^{37} + 60q^{40} + 36q^{41} - 24q^{42} + 36q^{43} + 64q^{44} + 52q^{46} + 14q^{49} + 40q^{50} - 24q^{51} + 32q^{53} - 12q^{55} - 36q^{56} + 38q^{57} + 72q^{58} + 44q^{60} - 72q^{62} - 4q^{63} - 18q^{67} + 144q^{68} + 152q^{70} - 36q^{71} + 38q^{73} + 40q^{74} - 14q^{75} + 76q^{76} - 96q^{80} + 820q^{81} - 96q^{82} - 48q^{83} - 72q^{84} - 4q^{85} + 48q^{86} - 36q^{87} - 48q^{89} - 200q^{92} + 14q^{93} - 48q^{95} - 12q^{96} + 98q^{97} + 72q^{98} + 8q^{99} + O(q^{100}) \)

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

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