Properties

Label 165.3.g
Level $165$
Weight $3$
Character orbit 165.g
Rep. character $\chi_{165}(89,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $3$
Sturm bound $72$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 165.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(165, [\chi])\).

Total New Old
Modular forms 52 40 12
Cusp forms 44 40 4
Eisenstein series 8 0 8

Trace form

\( 40 q + 84 q^{4} - 8 q^{6} - 26 q^{9} - 16 q^{10} + 31 q^{15} + 148 q^{16} + 40 q^{19} + 4 q^{21} - 188 q^{24} - 70 q^{25} + 34 q^{30} - 52 q^{31} - 16 q^{34} + 24 q^{36} + 152 q^{39} - 4 q^{40} - 49 q^{45}+ \cdots + 110 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.3.g.a 165.g 15.d $2$ $4.496$ \(\Q(\sqrt{-11}) \) None 165.3.g.a \(-2\) \(-5\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-2-\beta )q^{3}-3q^{4}-5q^{5}+\cdots\)
165.3.g.b 165.g 15.d $2$ $4.496$ \(\Q(\sqrt{-11}) \) None 165.3.g.a \(2\) \(5\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(3-\beta )q^{3}-3q^{4}+5q^{5}+(3+\cdots)q^{6}+\cdots\)
165.3.g.c 165.g 15.d $36$ $4.496$ None 165.3.g.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(165, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)