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Properties

Label 3528.2.fe
Level $3528$
Weight $2$
Character orbit 3528.fe
Rep. character $\chi_{3528}(11,\cdot)$
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.fe (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

\( 8016 q - 21 q^{2} - 26 q^{3} - 5 q^{4} - 12 q^{6} - 26 q^{9} + O(q^{10}) \) \( 8016 q - 21 q^{2} - 26 q^{3} - 5 q^{4} - 12 q^{6} - 26 q^{9} - 22 q^{10} - 36 q^{11} + 64 q^{12} + 72 q^{14} - 5 q^{16} - 9 q^{18} - 24 q^{19} - 15 q^{20} - 9 q^{22} - 6 q^{24} + 636 q^{25} + 6 q^{26} - 20 q^{27} - 28 q^{28} - 20 q^{30} - 21 q^{32} - 14 q^{33} - 3 q^{34} - 30 q^{35} + 14 q^{36} - 18 q^{38} - 13 q^{40} - 30 q^{41} + 6 q^{42} - 10 q^{43} - 9 q^{44} - 22 q^{46} - 23 q^{48} - 12 q^{49} - 21 q^{50} + 6 q^{51} - 16 q^{52} - 61 q^{54} + 3 q^{56} + 10 q^{57} - 4 q^{58} - 42 q^{59} - 91 q^{60} + 42 q^{62} - 20 q^{64} - 42 q^{65} + 54 q^{66} - 24 q^{67} + 21 q^{68} - 4 q^{70} - 32 q^{72} - 52 q^{73} - 6 q^{74} - 58 q^{75} + 47 q^{76} - 139 q^{78} - 87 q^{80} + 14 q^{81} - 24 q^{82} + 30 q^{83} - 109 q^{84} + 36 q^{86} + 24 q^{89} - 168 q^{90} - 20 q^{91} + 15 q^{92} + 11 q^{94} - 44 q^{96} - 24 q^{97} - 57 q^{98} - 66 q^{99} + O(q^{100}) \)

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.