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Properties

Label 3528.2.ev
Level $3528$
Weight $2$
Character orbit 3528.ev
Rep. character $\chi_{3528}(461,\cdot)$
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.ev (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

\( 8016 q - 15 q^{2} - 5 q^{4} - 14 q^{6} - 12 q^{7} - 20 q^{9} + O(q^{10}) \) \( 8016 q - 15 q^{2} - 5 q^{4} - 14 q^{6} - 12 q^{7} - 20 q^{9} - 28 q^{10} - 49 q^{12} + 72 q^{14} - 8 q^{15} - 5 q^{16} - 10 q^{18} - 21 q^{20} - 13 q^{22} - 30 q^{23} - 14 q^{24} - 662 q^{25} - 32 q^{28} + 2 q^{30} - 15 q^{32} - 28 q^{33} - 7 q^{34} + 22 q^{36} - 63 q^{38} - 32 q^{39} - 7 q^{40} - 42 q^{41} - 14 q^{42} - 12 q^{46} - 42 q^{47} - 12 q^{49} - 6 q^{50} - 7 q^{52} - 14 q^{54} - 56 q^{55} + 3 q^{56} - 80 q^{57} - 13 q^{58} - 72 q^{60} + 2 q^{63} - 20 q^{64} - 30 q^{65} + 154 q^{66} - q^{70} - 20 q^{72} - 56 q^{73} - 27 q^{74} - 35 q^{76} - 42 q^{78} - 24 q^{79} - 60 q^{81} - 28 q^{82} + 212 q^{84} + 93 q^{86} - 28 q^{87} + 11 q^{88} + 154 q^{90} + 135 q^{92} - 7 q^{94} - 180 q^{95} - 385 q^{96} + O(q^{100}) \)

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.