Properties

Label 1521.2.bk
Level $1521$
Weight $2$
Character orbit 1521.bk
Rep. character $\chi_{1521}(61,\cdot)$
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.bk (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

\( 4320 q - 14 q^{2} - 25 q^{3} + 164 q^{4} - 11 q^{5} - 35 q^{6} - 7 q^{7} - 34 q^{8} - 23 q^{9} + O(q^{10}) \) \( 4320 q - 14 q^{2} - 25 q^{3} + 164 q^{4} - 11 q^{5} - 35 q^{6} - 7 q^{7} - 34 q^{8} - 23 q^{9} - 52 q^{10} - 10 q^{11} - 23 q^{12} - 15 q^{14} + 18 q^{15} + 158 q^{16} - 58 q^{17} + 21 q^{18} - 23 q^{19} - 35 q^{20} - q^{21} + 4 q^{22} - 304 q^{23} + 58 q^{24} + 161 q^{25} - 40 q^{26} - 22 q^{27} - 52 q^{28} - 25 q^{29} - 71 q^{30} - 7 q^{31} + 124 q^{32} - 10 q^{33} - 13 q^{34} - 76 q^{35} - 75 q^{36} - 49 q^{37} - 57 q^{38} + 35 q^{39} - q^{40} - 3 q^{41} - 10 q^{42} - 19 q^{43} - 122 q^{44} + 44 q^{45} - 72 q^{46} + 174 q^{47} + 15 q^{48} - 343 q^{49} - 53 q^{50} - 157 q^{51} - 7 q^{52} - 32 q^{53} - 104 q^{54} - 55 q^{55} + 27 q^{56} - 74 q^{57} - 4 q^{58} + 6 q^{59} - 77 q^{60} - 25 q^{61} - 77 q^{62} + 41 q^{63} - 346 q^{64} - 32 q^{65} - 159 q^{66} - 25 q^{67} - 13 q^{68} - 86 q^{69} - 53 q^{70} - 66 q^{71} + 98 q^{72} - 58 q^{73} + 61 q^{74} - 131 q^{75} + 61 q^{76} - 25 q^{77} - 91 q^{78} - 16 q^{79} - 10 q^{80} - 19 q^{81} - 43 q^{82} - 110 q^{83} + 135 q^{84} - 13 q^{85} - 85 q^{86} - 55 q^{87} + 64 q^{88} - 155 q^{89} - 57 q^{90} - 46 q^{91} - 221 q^{92} - 24 q^{93} - 55 q^{94} + 83 q^{95} + 222 q^{96} + 35 q^{97} + 9 q^{98} - 70 q^{99} + O(q^{100}) \)

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

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