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Properties

Label 528.6.u
Level $528$
Weight $6$
Character orbit 528.u
Rep. character $\chi_{528}(155,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $800$
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.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 968 800 168
Cusp forms 952 800 152
Eisenstein series 16 0 16

Trace form

\( 800 q + 228 q^{6} + O(q^{10}) \) \( 800 q + 228 q^{6} + 200 q^{10} - 1572 q^{12} - 2440 q^{16} + 8020 q^{18} - 4720 q^{19} + 11020 q^{24} + 7464 q^{27} - 1388 q^{30} - 52248 q^{34} + 65588 q^{36} + 89808 q^{39} - 888 q^{40} - 38400 q^{42} - 125720 q^{46} + 65352 q^{48} + 1920800 q^{49} - 16360 q^{51} - 71576 q^{58} + 190308 q^{60} - 96160 q^{61} + 209592 q^{64} - 99220 q^{66} - 378600 q^{70} - 278264 q^{72} + 127736 q^{75} + 167624 q^{76} - 180928 q^{78} + 353312 q^{82} - 104956 q^{84} + 264800 q^{85} - 564368 q^{87} - 324188 q^{90} - 362352 q^{93} + 410640 q^{94} + 427532 q^{96} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(528, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)