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Properties

Label 3528.2.ft
Level $3528$
Weight $2$
Character orbit 3528.ft
Rep. character $\chi_{3528}(139,\cdot)$
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.ft (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

\( 8016 q - 5 q^{2} - 28 q^{3} - 5 q^{4} - 14 q^{6} - 20 q^{8} - 20 q^{9} + O(q^{10}) \) \( 8016 q - 5 q^{2} - 28 q^{3} - 5 q^{4} - 14 q^{6} - 20 q^{8} - 20 q^{9} - 28 q^{10} - 10 q^{11} - 49 q^{12} - 32 q^{14} - 5 q^{16} - 56 q^{17} - 18 q^{18} - 7 q^{20} - 13 q^{22} - 14 q^{24} + 642 q^{25} - 28 q^{26} - 28 q^{27} - 16 q^{28} - 42 q^{30} + 15 q^{32} - 28 q^{33} - 7 q^{34} - 68 q^{35} + 22 q^{36} + 7 q^{38} - 7 q^{40} - 14 q^{41} - 24 q^{42} - 10 q^{43} + 8 q^{44} - 12 q^{46} - 12 q^{49} - 10 q^{50} - 4 q^{51} - 7 q^{52} - 14 q^{54} + 93 q^{56} + 40 q^{57} + 3 q^{58} - 14 q^{59} + 64 q^{60} - 20 q^{64} - 50 q^{65} + 14 q^{66} - 24 q^{67} - 7 q^{70} + 44 q^{72} - 56 q^{73} + 47 q^{74} - 28 q^{75} + 21 q^{76} - 18 q^{78} + 20 q^{81} - 28 q^{82} - 14 q^{83} + 100 q^{84} - 49 q^{86} + 11 q^{88} - 56 q^{89} + 84 q^{90} - 76 q^{91} + 61 q^{92} - 7 q^{94} + 119 q^{96} + 104 q^{98} - 84 q^{99} + O(q^{100}) \)

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.