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Properties

Label 3549.2.em
Level $3549$
Weight $2$
Character orbit 3549.em
Rep. character $\chi_{3549}(2,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $23088$
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.em (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3549 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 23472 23472 0
Cusp forms 23088 23088 0
Eisenstein series 384 384 0

Trace form

\( 23088 q - 28 q^{3} - 52 q^{4} - 100 q^{6} - 96 q^{7} - 28 q^{9} + O(q^{10}) \) \( 23088 q - 28 q^{3} - 52 q^{4} - 100 q^{6} - 96 q^{7} - 28 q^{9} - 40 q^{10} - 62 q^{12} - 192 q^{13} - 98 q^{15} + 1820 q^{16} - 24 q^{18} - 32 q^{19} - 46 q^{21} - 96 q^{22} - 28 q^{24} - 52 q^{25} - 88 q^{27} - 172 q^{28} + 164 q^{30} - 94 q^{31} - 10 q^{33} - 160 q^{34} - 44 q^{36} - 66 q^{37} + 172 q^{39} - 96 q^{40} - 62 q^{42} - 100 q^{43} - 24 q^{45} - 444 q^{46} - 80 q^{48} - 48 q^{49} + 10 q^{51} - 92 q^{52} - 40 q^{54} - 200 q^{55} - 114 q^{57} - 96 q^{58} + 32 q^{60} - 56 q^{61} - 202 q^{63} - 208 q^{64} - 90 q^{66} - 208 q^{67} - 128 q^{69} + 208 q^{70} - 72 q^{72} + 30 q^{73} - 286 q^{75} - 324 q^{76} - 186 q^{78} - 20 q^{79} - 16 q^{81} - 88 q^{82} - 224 q^{84} - 264 q^{85} + 34 q^{87} - 392 q^{88} - 104 q^{90} - 128 q^{91} - 72 q^{93} + 276 q^{94} + 64 q^{96} - 270 q^{97} - 94 q^{99} + O(q^{100}) \)

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.