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Properties

Label 3549.2.dr
Level $3549$
Weight $2$
Character orbit 3549.dr
Rep. character $\chi_{3549}(101,\cdot)$
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.dr (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

\( 11544 q - 39 q^{3} + 448 q^{4} - 45 q^{7} - 7 q^{9} + O(q^{10}) \) \( 11544 q - 39 q^{3} + 448 q^{4} - 45 q^{7} - 7 q^{9} - 78 q^{10} - 27 q^{12} + 120 q^{13} + 9 q^{15} + 434 q^{16} - 49 q^{18} - 158 q^{19} - 35 q^{21} - 34 q^{22} - 15 q^{24} - 485 q^{25} - 60 q^{28} - 97 q^{30} - 49 q^{31} - 9 q^{33} - 24 q^{34} - 52 q^{36} + q^{37} - 50 q^{39} - 24 q^{40} - 28 q^{42} - 100 q^{43} - 36 q^{45} - 106 q^{46} - 42 q^{48} - 67 q^{49} + 7 q^{51} - 82 q^{52} + 186 q^{54} + 30 q^{55} - 91 q^{57} + 78 q^{58} - 22 q^{60} - 78 q^{61} + 113 q^{63} - 956 q^{64} - 286 q^{67} - 156 q^{69} + 228 q^{70} - 13 q^{72} - 100 q^{73} + 144 q^{75} - 296 q^{76} - 41 q^{78} - 13 q^{79} - 47 q^{81} - 78 q^{82} - 285 q^{84} - 74 q^{85} - 42 q^{87} + 122 q^{88} - 57 q^{91} - 16 q^{93} - 312 q^{94} - 63 q^{96} + 7 q^{97} + O(q^{100}) \)

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.