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Properties

Label 3528.2.ef
Level $3528$
Weight $2$
Character orbit 3528.ef
Rep. character $\chi_{3528}(85,\cdot)$
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.ef (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

\( 8016 q - 5 q^{2} - 5 q^{4} - 6 q^{6} - 12 q^{7} - 20 q^{8} - 20 q^{9} + O(q^{10}) \) \( 8016 q - 5 q^{2} - 5 q^{4} - 6 q^{6} - 12 q^{7} - 20 q^{8} - 20 q^{9} - 12 q^{10} - 29 q^{12} + 20 q^{14} - 8 q^{15} - 5 q^{16} - 40 q^{17} - 38 q^{18} + 11 q^{20} + 3 q^{22} - 10 q^{23} - 2 q^{24} - 662 q^{25} - 12 q^{26} - 32 q^{28} - 30 q^{30} - 24 q^{31} - 25 q^{32} - 8 q^{33} - q^{34} - 58 q^{36} - 15 q^{38} - 8 q^{39} - 15 q^{40} - 10 q^{41} - 2 q^{42} - 48 q^{44} - 28 q^{46} - 50 q^{47} - 82 q^{48} - 12 q^{49} - 30 q^{50} + 11 q^{52} + 38 q^{54} + 107 q^{56} + 40 q^{57} + 3 q^{58} + 68 q^{60} + 88 q^{62} - 78 q^{63} - 20 q^{64} + 30 q^{65} - 16 q^{66} - 14 q^{68} + 9 q^{70} - 40 q^{71} + 44 q^{72} - 40 q^{73} + 47 q^{74} + 15 q^{76} - 102 q^{78} - 24 q^{79} + 48 q^{80} - 60 q^{81} - 28 q^{82} - 106 q^{84} - 33 q^{86} - 8 q^{87} - 21 q^{88} - 72 q^{89} - 126 q^{90} + 29 q^{92} - 13 q^{94} + 40 q^{95} - 71 q^{96} - 24 q^{97} - 116 q^{98} + O(q^{100}) \)

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.