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Properties

Label 3549.2.cy
Level $3549$
Weight $2$
Character orbit 3549.cy
Rep. character $\chi_{3549}(17,\cdot)$
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.cy (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

\( 11544 q - 36 q^{3} - 974 q^{4} - 50 q^{7} - 16 q^{9} + O(q^{10}) \) \( 11544 q - 36 q^{3} - 974 q^{4} - 50 q^{7} - 16 q^{9} - 72 q^{10} - 27 q^{12} - 120 q^{13} + 9 q^{15} - 946 q^{16} + 23 q^{18} - 79 q^{19} - 17 q^{21} - 34 q^{22} - 27 q^{24} - 485 q^{25} - 62 q^{28} + 107 q^{30} - 107 q^{31} - 24 q^{33} + 24 q^{34} - 52 q^{36} - 26 q^{37} + 103 q^{39} - 24 q^{40} - 61 q^{42} - 100 q^{43} - 33 q^{45} + 182 q^{46} + 42 q^{48} - 52 q^{49} + 7 q^{51} - 26 q^{52} + 177 q^{54} - 30 q^{55} - 91 q^{57} - 108 q^{58} - 4 q^{60} - 111 q^{61} - 91 q^{63} - 956 q^{64} + 117 q^{66} + 155 q^{67} + 156 q^{69} - 228 q^{70} + 110 q^{72} - 56 q^{73} - 39 q^{75} + 296 q^{76} - 41 q^{78} - 13 q^{79} + 4 q^{81} - 12 q^{82} + 447 q^{84} - 74 q^{85} - 39 q^{87} - 100 q^{88} - 174 q^{91} - 13 q^{93} - 162 q^{94} - 15 q^{96} - 7 q^{97} + O(q^{100}) \)

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.