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Properties

Label 165.6.k
Level $165$
Weight $6$
Character orbit 165.k
Rep. character $\chi_{165}(23,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $200$
Sturm bound $144$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 165.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(165, [\chi])\).

Total New Old
Modular forms 248 200 48
Cusp forms 232 200 32
Eisenstein series 16 0 16

Trace form

\( 200 q - 2 q^{3} + 160 q^{6} + O(q^{10}) \) \( 200 q - 2 q^{3} + 160 q^{6} + 128 q^{12} + 3184 q^{13} + 4084 q^{15} - 52360 q^{16} - 12132 q^{18} - 880 q^{21} - 6612 q^{25} + 23044 q^{27} + 22432 q^{28} + 39256 q^{30} + 33440 q^{31} + 7502 q^{33} - 36480 q^{36} - 65196 q^{37} - 62312 q^{40} + 133256 q^{42} + 33848 q^{45} + 260400 q^{46} - 120664 q^{48} - 39920 q^{51} - 254392 q^{52} - 27588 q^{55} + 213400 q^{57} + 296968 q^{58} + 148600 q^{60} + 304800 q^{61} - 133676 q^{63} - 48188 q^{67} - 656360 q^{70} + 350568 q^{72} + 252000 q^{73} + 118516 q^{75} + 415680 q^{76} - 1026760 q^{78} - 277660 q^{81} - 476792 q^{82} + 258632 q^{85} + 572176 q^{87} + 229416 q^{88} - 53056 q^{90} + 532560 q^{91} + 148918 q^{93} - 466360 q^{96} - 492364 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)