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Properties

Label 528.6.bo
Level $528$
Weight $6$
Character orbit 528.bo
Rep. character $\chi_{528}(29,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3808$
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.bo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 528 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 3872 3872 0
Cusp forms 3808 3808 0
Eisenstein series 64 64 0

Trace form

\( 3808 q - 6 q^{3} - 12 q^{4} - 10 q^{6} + O(q^{10}) \) \( 3808 q - 6 q^{3} - 12 q^{4} - 10 q^{6} - 16 q^{12} - 20 q^{13} - 12 q^{15} - 6700 q^{16} - 10 q^{18} - 20 q^{19} - 22920 q^{22} - 10 q^{24} - 6 q^{27} - 20 q^{28} - 10 q^{30} - 24 q^{31} - 16 q^{33} + 224 q^{34} - 4102 q^{36} - 12 q^{37} - 20 q^{40} + 15878 q^{42} + 12484 q^{45} - 660 q^{46} + 47014 q^{48} - 2170528 q^{49} - 10 q^{51} + 196020 q^{52} + 80596 q^{58} - 19010 q^{60} - 20 q^{61} - 20 q^{63} - 281172 q^{64} + 9706 q^{66} + 97824 q^{67} - 1464 q^{69} - 129960 q^{70} + 449840 q^{72} - 13478 q^{75} + 154868 q^{78} - 40 q^{79} - 12 q^{81} - 72208 q^{82} + 168060 q^{84} - 20 q^{85} - 1492076 q^{88} - 590500 q^{90} + 434612 q^{91} + 966 q^{93} + 309700 q^{94} - 10 q^{96} - 24 q^{97} + 287850 q^{99} + O(q^{100}) \)

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.