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Properties

Label 165.6.j
Level $165$
Weight $6$
Character orbit 165.j
Rep. character $\chi_{165}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
Sturm bound $144$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 165.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 248 120 128
Cusp forms 232 120 112
Eisenstein series 16 0 16

Trace form

\( 120 q + 88 q^{5} + O(q^{10}) \) \( 120 q + 88 q^{5} - 40 q^{11} - 1584 q^{12} + 792 q^{15} - 32240 q^{16} - 13640 q^{20} - 2908 q^{22} + 10208 q^{23} + 13992 q^{25} - 8400 q^{26} - 9680 q^{31} - 15624 q^{33} - 155520 q^{36} - 37048 q^{37} - 74536 q^{38} + 34848 q^{42} - 52800 q^{47} - 50688 q^{48} + 63624 q^{53} + 47480 q^{55} - 401200 q^{56} + 316736 q^{58} - 50688 q^{60} - 91080 q^{66} + 213408 q^{67} + 262112 q^{70} + 143840 q^{71} + 77760 q^{75} + 412584 q^{77} + 151416 q^{78} - 471720 q^{80} - 787320 q^{81} - 313992 q^{82} - 676400 q^{86} - 456956 q^{88} + 990320 q^{91} + 186880 q^{92} + 4752 q^{93} + 77528 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)