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Properties

Label 3528.2.y
Level $3528$
Weight $2$
Character orbit 3528.y
Rep. character $\chi_{3528}(1685,\cdot)$
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.y (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

\( 944 q + 3 q^{2} - q^{4} - 6 q^{6} + 2 q^{9} + O(q^{10}) \) \( 944 q + 3 q^{2} - q^{4} - 6 q^{6} + 2 q^{9} + 6 q^{10} + 3 q^{12} - 22 q^{15} - q^{16} + 3 q^{18} + 12 q^{24} - 876 q^{25} - 6 q^{26} + 52 q^{30} + 6 q^{31} + 63 q^{32} + 6 q^{33} + 6 q^{34} - 44 q^{36} + 66 q^{38} - 10 q^{39} - 81 q^{44} + 10 q^{46} + 6 q^{47} + 9 q^{48} - 27 q^{50} - 24 q^{54} - 28 q^{57} - 6 q^{58} + 36 q^{60} + 12 q^{62} - 16 q^{64} + 6 q^{65} + 21 q^{66} + 36 q^{68} - 33 q^{72} + 12 q^{73} + 12 q^{76} + 19 q^{78} - 2 q^{79} - 57 q^{80} - 6 q^{81} - 12 q^{87} + 18 q^{88} - 24 q^{89} - 75 q^{90} + 18 q^{92} + 3 q^{94} + 126 q^{95} + 54 q^{96} + O(q^{100}) \)

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.

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

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