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Properties

Label 1521.2.bi
Level $1521$
Weight $2$
Character orbit 1521.bi
Rep. character $\chi_{1521}(16,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $4320$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1521.bi (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1521 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 4416 4416 0
Cusp forms 4320 4320 0
Eisenstein series 96 96 0

Trace form

\( 4320 q - 11 q^{2} - 25 q^{3} - 367 q^{4} - 11 q^{5} - 14 q^{6} - 16 q^{7} - 34 q^{8} - 23 q^{9} + O(q^{10}) \) \( 4320 q - 11 q^{2} - 25 q^{3} - 367 q^{4} - 11 q^{5} - 14 q^{6} - 16 q^{7} - 34 q^{8} - 23 q^{9} - 52 q^{10} - 19 q^{11} - 23 q^{12} - 15 q^{14} + 15 q^{15} - 355 q^{16} - 58 q^{17} + 21 q^{18} - 23 q^{19} - 2 q^{20} - q^{21} - 8 q^{22} + 152 q^{23} + 64 q^{24} + 161 q^{25} - 40 q^{26} - 22 q^{27} - 52 q^{28} + 11 q^{29} + 118 q^{30} - 7 q^{31} - 53 q^{32} - 37 q^{33} - 13 q^{34} - 76 q^{35} + 12 q^{36} - 49 q^{37} + 21 q^{38} - 133 q^{39} - q^{40} - 18 q^{41} - 43 q^{42} - 10 q^{43} - 122 q^{44} + 20 q^{45} - 72 q^{46} - 21 q^{47} + 152 q^{49} + 7 q^{50} + 38 q^{51} + 11 q^{52} - 32 q^{53} - 221 q^{54} - 55 q^{55} - 33 q^{56} + 43 q^{57} - 31 q^{58} - 51 q^{59} - 77 q^{60} - 7 q^{61} - 77 q^{62} - 169 q^{63} - 346 q^{64} - 11 q^{65} - 276 q^{66} - 7 q^{67} - 13 q^{68} + 28 q^{69} - 53 q^{70} - 66 q^{71} - 346 q^{72} - 58 q^{73} - 50 q^{74} + 70 q^{75} - 50 q^{76} - 25 q^{77} - 106 q^{78} - 16 q^{79} - 10 q^{80} - 7 q^{81} - 43 q^{82} - 110 q^{83} + 216 q^{84} - 13 q^{85} - 85 q^{86} + 14 q^{87} - 167 q^{88} - 155 q^{89} - 57 q^{90} - 46 q^{91} + 91 q^{92} + 123 q^{93} + 8 q^{94} - 10 q^{95} + 222 q^{96} - 37 q^{97} + 9 q^{98} - 70 q^{99} + O(q^{100}) \)

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.