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Properties

Label 3528.2.dy
Level $3528$
Weight $2$
Character orbit 3528.dy
Rep. character $\chi_{3528}(187,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $8016$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.dy (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3528 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3528, [\chi])\).

Total New Old
Modular forms 8112 8112 0
Cusp forms 8016 8016 0
Eisenstein series 96 96 0

Trace form

\( 8016 q - 8 q^{2} - 22 q^{3} - 8 q^{4} - 20 q^{6} - 20 q^{8} - 26 q^{9} + O(q^{10}) \) \( 8016 q - 8 q^{2} - 22 q^{3} - 8 q^{4} - 20 q^{6} - 20 q^{8} - 26 q^{9} - 22 q^{10} - 10 q^{11} - 46 q^{12} + 58 q^{14} - 8 q^{16} - 44 q^{17} - 72 q^{19} + 17 q^{20} - q^{22} - 2 q^{24} - 1314 q^{25} - 28 q^{26} - 28 q^{27} - 28 q^{28} + 9 q^{30} - 18 q^{32} - 22 q^{33} - 13 q^{34} - 38 q^{35} - 26 q^{36} - 35 q^{38} - 7 q^{40} - 14 q^{41} - 39 q^{42} - 10 q^{43} - 7 q^{44} - 30 q^{46} - 9 q^{48} - 12 q^{49} - 13 q^{50} + 26 q^{51} - 7 q^{52} + 16 q^{54} - 267 q^{56} - 50 q^{57} + 3 q^{58} - 8 q^{59} - 170 q^{60} - 42 q^{62} - 20 q^{64} + 4 q^{65} - 259 q^{66} + 12 q^{67} + 17 q^{70} + 17 q^{72} - 44 q^{73} + 59 q^{74} + 8 q^{75} + 9 q^{76} + 81 q^{78} + 21 q^{80} - 130 q^{81} - 16 q^{82} + 46 q^{83} + 181 q^{84} - 49 q^{86} + 11 q^{88} - 20 q^{89} + 51 q^{90} - 76 q^{91} + 67 q^{92} - 4 q^{94} - 205 q^{96} - 55 q^{98} - 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces

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