Properties

Label 3549.2.de
Level $3549$
Weight $2$
Character orbit 3549.de
Rep. character $\chi_{3549}(88,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $5832$
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.de (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 11736 5832 5904
Cusp forms 11544 5832 5712
Eisenstein series 192 0 192

Trace form

\( 5832q + 6q^{3} - 244q^{4} + q^{7} - 486q^{9} + O(q^{10}) \) \( 5832q + 6q^{3} - 244q^{4} + q^{7} - 486q^{9} - 16q^{10} + 8q^{12} - 24q^{13} + 20q^{14} + 238q^{16} + 24q^{20} - 7q^{21} - 6q^{22} - 245q^{25} - 22q^{26} + 6q^{27} + 44q^{28} - 3q^{31} + 130q^{32} + 14q^{35} - 244q^{36} + 15q^{37} + 500q^{38} + 8q^{39} - 14q^{40} - 18q^{41} + 152q^{42} + 12q^{44} - 12q^{46} + 36q^{47} - 18q^{48} + 181q^{49} + 102q^{50} - 4q^{51} + 44q^{52} - 400q^{53} - 26q^{55} - 18q^{56} - 104q^{58} - 160q^{59} + 36q^{60} + 26q^{61} + 48q^{62} + q^{63} + 468q^{64} - 8q^{65} - 16q^{66} - 156q^{67} - 110q^{68} + 16q^{69} + 348q^{70} + 138q^{71} - 42q^{73} + 404q^{74} + 13q^{75} - 156q^{76} - 42q^{77} + 18q^{78} - 19q^{79} - 486q^{81} + 12q^{82} - 50q^{84} - 160q^{85} - 276q^{86} - 18q^{87} + 48q^{89} - 16q^{90} + 75q^{91} - 108q^{92} + 127q^{93} + 174q^{94} + 104q^{95} - 30q^{96} + 129q^{97} + 30q^{98} + O(q^{100}) \)

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

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