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Properties

Label 528.6.b
Level $528$
Weight $6$
Character orbit 528.b
Rep. character $\chi_{528}(65,\cdot)$
Character field $\Q$
Dimension $118$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 528.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(528, [\chi])\).

Total New Old
Modular forms 492 122 370
Cusp forms 468 118 350
Eisenstein series 24 4 20

Trace form

\( 118 q + 2 q^{3} - 46 q^{9} + O(q^{10}) \) \( 118 q + 2 q^{3} - 46 q^{9} - 1918 q^{15} - 66026 q^{25} - 2152 q^{27} + 4 q^{31} - 3554 q^{33} - 4 q^{37} + 6248 q^{45} - 272902 q^{49} + 28956 q^{55} - 53764 q^{67} - 62700 q^{69} + 75604 q^{75} + 10602 q^{81} - 167280 q^{91} + 147528 q^{93} + 298668 q^{97} + 126170 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(528, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(528, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)