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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

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

Display 100 coefficients 10 coefficients

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

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