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Properties

Label 1521.2.by
Level $1521$
Weight $2$
Character orbit 1521.by
Rep. character $\chi_{1521}(4,\cdot)$
Character field $\Q(\zeta_{78})$
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.by (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1521 \)
Character field: \(\Q(\zeta_{78})\)
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

\( 4320 q - 13 q^{2} - 25 q^{3} + 345 q^{4} - 13 q^{5} - 14 q^{6} - 10 q^{7} - 52 q^{8} - 27 q^{9} + O(q^{10}) \) \( 4320 q - 13 q^{2} - 25 q^{3} + 345 q^{4} - 13 q^{5} - 14 q^{6} - 10 q^{7} - 52 q^{8} - 27 q^{9} - 48 q^{10} - 13 q^{11} - 15 q^{12} - 24 q^{13} - 7 q^{14} - 69 q^{15} - 363 q^{16} - 58 q^{17} - 95 q^{18} - 69 q^{19} + 14 q^{20} - 11 q^{21} - 40 q^{22} + 160 q^{23} + 22 q^{24} - 183 q^{25} - 52 q^{26} - 34 q^{27} - 52 q^{28} - 49 q^{29} - 76 q^{30} - q^{31} + 65 q^{32} - 35 q^{33} - 19 q^{34} - 34 q^{35} - 8 q^{36} - 49 q^{37} - 79 q^{38} - 137 q^{39} - 29 q^{40} + 2 q^{41} - 7 q^{42} - 10 q^{43} - 78 q^{44} + 42 q^{45} - 72 q^{46} - 159 q^{47} - 42 q^{48} - 184 q^{49} - 25 q^{50} - 118 q^{51} + 7 q^{52} - 40 q^{53} + 127 q^{54} - 45 q^{55} - 27 q^{56} - 59 q^{57} - 13 q^{58} - 13 q^{59} - 35 q^{60} - 21 q^{61} - 61 q^{62} - 93 q^{63} + 310 q^{64} + 53 q^{65} + 92 q^{66} + 11 q^{67} + 53 q^{68} - 4 q^{69} + 15 q^{70} - 46 q^{71} + 336 q^{72} - 52 q^{73} - 6 q^{74} - 64 q^{75} + 18 q^{76} - 53 q^{77} - 26 q^{78} - 18 q^{79} - 168 q^{80} - 71 q^{81} - 57 q^{82} + 66 q^{83} - 342 q^{84} - 13 q^{85} - 55 q^{86} - 12 q^{87} - 207 q^{88} - 75 q^{89} - 37 q^{90} - 58 q^{91} + 87 q^{92} + 15 q^{93} - 36 q^{94} + 84 q^{95} + 170 q^{96} - 13 q^{97} - 157 q^{98} - 18 q^{99} + O(q^{100}) \)

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.