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Properties

Label 3528.2.c
Level $3528$
Weight $2$
Character orbit 3528.c
Rep. character $\chi_{3528}(1765,\cdot)$
Character field $\Q$
Dimension $200$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 704 210 494
Cusp forms 640 200 440
Eisenstein series 64 10 54

Trace form

\( 200 q - 2 q^{2} + 4 q^{8} + O(q^{10}) \) \( 200 q - 2 q^{2} + 4 q^{8} - 4 q^{16} + 16 q^{20} - 4 q^{22} - 4 q^{23} - 180 q^{25} - 8 q^{26} - 12 q^{32} - 2 q^{34} + 18 q^{38} - 20 q^{40} - 8 q^{41} - 44 q^{44} - 24 q^{47} + 34 q^{50} + 36 q^{52} - 20 q^{62} + 12 q^{64} - 26 q^{68} + 8 q^{71} + 4 q^{73} + 8 q^{74} - 6 q^{76} - 4 q^{79} + 56 q^{80} - 10 q^{82} - 20 q^{86} + 52 q^{88} + 20 q^{92} - 4 q^{95} + 4 q^{97} + O(q^{100}) \)

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

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