Properties

Label 165.6.c
Level $165$
Weight $6$
Character orbit 165.c
Rep. character $\chi_{165}(34,\cdot)$
Character field $\Q$
Dimension $52$
Newform subspaces $2$
Sturm bound $144$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 165.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(4\)

Dimensions

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

Total New Old
Modular forms 124 52 72
Cusp forms 116 52 64
Eisenstein series 8 0 8

Trace form

\( 52 q - 876 q^{4} - 196 q^{5} + 180 q^{6} - 4212 q^{9} - 1708 q^{10} + 6736 q^{14} + 15284 q^{16} + 80 q^{19} + 6524 q^{20} + 360 q^{21} - 540 q^{24} + 10996 q^{25} + 9864 q^{26} - 14208 q^{29} + 2736 q^{30}+ \cdots - 476100 q^{96}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.6.c.a 165.c 5.b $26$ $26.463$ None 165.6.c.a \(0\) \(0\) \(-98\) \(0\) $\mathrm{SU}(2)[C_{2}]$
165.6.c.b 165.c 5.b $26$ $26.463$ None 165.6.c.b \(0\) \(0\) \(-98\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{6}^{\mathrm{old}}(165, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)