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Properties

Label 3528.2.bm
Level $3528$
Weight $2$
Character orbit 3528.bm
Rep. character $\chi_{3528}(2627,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
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 1408 320 1088
Cusp forms 1280 320 960
Eisenstein series 128 0 128

Trace form

\( 320 q + O(q^{10}) \) \( 320 q - 8 q^{16} + 8 q^{22} - 160 q^{25} - 80 q^{34} + 52 q^{40} - 28 q^{46} - 28 q^{52} - 56 q^{58} + 72 q^{64} - 32 q^{67} + 16 q^{73} + 120 q^{76} + 28 q^{82} + 80 q^{88} - 12 q^{94} - 32 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)