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Properties

Label 528.6.bn
Level $528$
Weight $6$
Character orbit 528.bn
Rep. character $\chi_{528}(17,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $472$
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.bn (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1968 488 1480
Cusp forms 1872 472 1400
Eisenstein series 96 16 80

Trace form

\( 472 q + 3 q^{3} + 10 q^{7} + 41 q^{9} + O(q^{10}) \) \( 472 q + 3 q^{3} + 10 q^{7} + 41 q^{9} - 10 q^{13} + 1923 q^{15} + 10 q^{19} + 66016 q^{25} + 2157 q^{27} + 6 q^{31} - 8341 q^{33} - 6 q^{37} - 5695 q^{39} - 6258 q^{45} + 272892 q^{49} - 185695 q^{51} - 28946 q^{55} - 81495 q^{57} - 10 q^{61} + 5 q^{63} + 53784 q^{67} + 63910 q^{69} - 16430 q^{73} - 75599 q^{75} + 386490 q^{79} - 10607 q^{81} - 248850 q^{85} - 82850 q^{91} - 147533 q^{93} + 282782 q^{97} - 126165 q^{99} + O(q^{100}) \)

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

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