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Properties

Label 165.3.l
Level $165$
Weight $3$
Character orbit 165.l
Rep. character $\chi_{165}(32,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $7$
Sturm bound $72$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 165.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 7 \)
Sturm bound: \(72\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(2\), \(23\)

Dimensions

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

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88 q - 6 q^{3} + O(q^{10}) \) \( 88 q - 6 q^{3} - 36 q^{15} - 272 q^{16} + 52 q^{22} - 84 q^{25} + 60 q^{27} + 16 q^{31} - 22 q^{33} + 408 q^{36} - 220 q^{37} + 152 q^{42} - 232 q^{45} - 24 q^{48} + 96 q^{55} + 272 q^{58} + 256 q^{60} + 324 q^{67} - 240 q^{70} + 156 q^{75} + 688 q^{78} - 540 q^{81} + 104 q^{82} - 556 q^{88} - 688 q^{91} - 710 q^{93} - 124 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.3.l.a 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{10})\) None \(0\) \(-12\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-3q^{3}+\beta _{2}q^{4}+(-4-3\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.b 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}-\beta _{2}q^{4}+5\beta _{2}q^{5}+\cdots\)
165.3.l.c 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(\beta _{1}-3\beta _{2})q^{3}-4\beta _{2}q^{4}+(3\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.d 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+\beta _{2}q^{4}+(4+3\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.e 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) \(0\) \(10\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(3+\beta _{3})q^{3}+4\beta _{2}q^{4}+(-3\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.f 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{6})\) None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+3q^{3}-\beta _{2}q^{4}-5\beta _{2}q^{5}+\cdots\)
165.3.l.g 165.l 165.l $64$ $4.496$ None \(0\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$