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Properties

Label 3528.2.w
Level $3528$
Weight $2$
Character orbit 3528.w
Rep. character $\chi_{3528}(949,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $944$
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.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1376 976 400
Cusp forms 1312 944 368
Eisenstein series 64 32 32

Trace form

\( 944 q - q^{2} - q^{4} + 2 q^{6} - 16 q^{8} + 2 q^{9} + O(q^{10}) \) \( 944 q - q^{2} - q^{4} + 2 q^{6} - 16 q^{8} + 2 q^{9} - 2 q^{10} + 17 q^{12} - 22 q^{15} - q^{16} + 4 q^{17} - q^{18} - 6 q^{20} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 876 q^{25} + 4 q^{26} + 20 q^{30} - 2 q^{31} - 11 q^{32} - 22 q^{33} - 4 q^{36} - 10 q^{38} + 14 q^{39} - 8 q^{40} + 4 q^{41} + 7 q^{44} - 6 q^{46} - 42 q^{47} + 3 q^{48} + 45 q^{50} + 18 q^{52} + 58 q^{54} - 4 q^{55} - 4 q^{57} + 10 q^{58} + 24 q^{60} - 32 q^{62} - 16 q^{64} - 22 q^{65} - 79 q^{66} - 24 q^{68} - 32 q^{71} + 23 q^{72} + 4 q^{73} - 14 q^{74} + 6 q^{76} + 13 q^{78} - 2 q^{79} + 11 q^{80} - 6 q^{81} - 66 q^{86} - 4 q^{87} - 14 q^{88} - 4 q^{89} + 35 q^{90} + 70 q^{92} - 9 q^{94} + 38 q^{95} + 16 q^{96} + 4 q^{97} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)