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Properties

Label 1521.2.ce
Level $1521$
Weight $2$
Character orbit 1521.ce
Rep. character $\chi_{1521}(5,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $8640$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1521.ce (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1521 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1521, [\chi])\).

Total New Old
Modular forms 8832 8832 0
Cusp forms 8640 8640 0
Eisenstein series 192 192 0

Trace form

\( 8640 q - 72 q^{2} - 44 q^{3} - 26 q^{4} - 72 q^{5} - 50 q^{6} - 22 q^{7} - 44 q^{9} + O(q^{10}) \) \( 8640 q - 72 q^{2} - 44 q^{3} - 26 q^{4} - 72 q^{5} - 50 q^{6} - 22 q^{7} - 44 q^{9} - 104 q^{10} - 60 q^{11} - 52 q^{12} - 24 q^{13} - 66 q^{14} - 62 q^{15} - 370 q^{16} - 38 q^{18} - 100 q^{19} - 84 q^{20} - 74 q^{21} - 48 q^{22} - 328 q^{24} - 26 q^{25} - 68 q^{27} - 56 q^{28} - 66 q^{29} - 156 q^{30} - 32 q^{31} - 84 q^{32} - 62 q^{33} - 20 q^{34} - 52 q^{36} - 92 q^{37} - 78 q^{38} - 190 q^{39} - 38 q^{40} - 96 q^{41} - 56 q^{42} - 26 q^{43} - 256 q^{45} + 324 q^{47} - 64 q^{48} - 26 q^{49} - 204 q^{50} - 52 q^{51} - 34 q^{52} - 122 q^{54} - 88 q^{55} - 78 q^{56} - 68 q^{57} + 2 q^{58} - 36 q^{59} - 12 q^{60} - 22 q^{61} - 258 q^{63} - 104 q^{64} - 66 q^{65} + 106 q^{66} - 10 q^{67} - 18 q^{68} + 26 q^{69} - 22 q^{70} - 106 q^{72} - 124 q^{73} - 234 q^{74} + 208 q^{75} - 32 q^{76} - 78 q^{77} - 44 q^{78} + 2 q^{79} - 92 q^{81} - 104 q^{82} - 114 q^{83} - 194 q^{84} - 2 q^{85} - 12 q^{86} - 112 q^{87} + 182 q^{88} - 52 q^{90} - 112 q^{91} + 78 q^{92} - 256 q^{93} - 22 q^{94} - 78 q^{95} + 608 q^{96} - 2 q^{97} + 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.