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Properties

Label 3549.2.dk
Level $3549$
Weight $2$
Character orbit 3549.dk
Rep. character $\chi_{3549}(152,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $11544$
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.dk (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3549 \)
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 11736 0
Cusp forms 11544 11544 0
Eisenstein series 192 192 0

Trace form

\( 11544 q - 39 q^{3} - 504 q^{4} + 12 q^{6} - 43 q^{7} - 15 q^{9} + O(q^{10}) \) \( 11544 q - 39 q^{3} - 504 q^{4} + 12 q^{6} - 43 q^{7} - 15 q^{9} - 78 q^{10} - 39 q^{12} - 120 q^{13} - 95 q^{15} + 442 q^{16} - 15 q^{18} - 33 q^{21} - 62 q^{22} - 39 q^{24} + 441 q^{25} - 4 q^{28} - 61 q^{30} - 39 q^{31} - 39 q^{33} - 48 q^{36} - 37 q^{37} - 44 q^{39} - 168 q^{40} - 4 q^{42} - 92 q^{43} - 36 q^{45} - 130 q^{46} - 18 q^{48} - 67 q^{49} - 9 q^{51} - 118 q^{52} - 246 q^{54} - 30 q^{55} + 13 q^{57} - 70 q^{58} - 68 q^{60} - 78 q^{61} + 163 q^{63} + 860 q^{64} - 84 q^{66} - 116 q^{67} - 84 q^{69} - 20 q^{70} + 21 q^{72} - 138 q^{73} + 114 q^{75} + 324 q^{76} + 19 q^{78} - 55 q^{79} - 15 q^{81} - 78 q^{82} + 209 q^{84} - 102 q^{85} - 42 q^{87} + 90 q^{88} + 23 q^{91} - 26 q^{93} - 312 q^{94} - 69 q^{96} - 33 q^{97} - 126 q^{99} + O(q^{100}) \)

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.