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Properties

Label 1521.2.e
Level $1521$
Weight $2$
Character orbit 1521.e
Rep. character $\chi_{1521}(508,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $288$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1521.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 392 332 60
Cusp forms 336 288 48
Eisenstein series 56 44 12

Trace form

\( 288 q + 2 q^{2} + 4 q^{3} - 132 q^{4} + 2 q^{5} - 6 q^{6} - 12 q^{8} + 12 q^{9} + O(q^{10}) \) \( 288 q + 2 q^{2} + 4 q^{3} - 132 q^{4} + 2 q^{5} - 6 q^{6} - 12 q^{8} + 12 q^{9} + 6 q^{11} + 6 q^{12} - 26 q^{14} + 10 q^{15} - 108 q^{16} + 24 q^{17} - 22 q^{18} + 12 q^{19} - 10 q^{20} + 10 q^{21} - 6 q^{22} - 2 q^{23} + 12 q^{24} - 102 q^{25} - 32 q^{27} - 12 q^{29} + 62 q^{30} - 6 q^{31} + 14 q^{32} - 38 q^{33} + 6 q^{34} - 24 q^{35} - 6 q^{36} + 12 q^{37} + 26 q^{38} + 10 q^{41} - 70 q^{42} - 6 q^{43} + 16 q^{44} + 20 q^{45} + 12 q^{47} - 84 q^{49} + 38 q^{50} - 10 q^{51} + 8 q^{53} - 6 q^{54} - 12 q^{55} - 84 q^{56} + 12 q^{58} - 2 q^{59} + 12 q^{60} - 12 q^{61} - 28 q^{62} + 8 q^{63} + 96 q^{64} - 24 q^{66} - 12 q^{67} - 96 q^{68} + 14 q^{69} - 56 q^{71} + 66 q^{72} + 36 q^{73} + 42 q^{74} - 28 q^{75} - 6 q^{76} - 2 q^{77} - 80 q^{80} + 44 q^{81} + 60 q^{82} - 2 q^{84} - 6 q^{86} + 42 q^{87} - 18 q^{88} - 56 q^{89} + 46 q^{90} - 58 q^{92} - 72 q^{93} - 12 q^{94} - 60 q^{95} + 148 q^{96} - 24 q^{97} + 124 q^{98} - 12 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1521, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)