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Properties

Label 165.2.k
Level $165$
Weight $2$
Character orbit 165.k
Rep. character $\chi_{165}(23,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $4$
Sturm bound $48$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(165, [\chi])\).

Total New Old
Modular forms 56 40 16
Cusp forms 40 40 0
Eisenstein series 16 0 16

Trace form

\( 40 q - 2 q^{3} - 8 q^{6} + O(q^{10}) \) \( 40 q - 2 q^{3} - 8 q^{6} + 8 q^{12} - 16 q^{13} + 4 q^{15} - 32 q^{16} - 12 q^{18} - 16 q^{21} - 12 q^{25} + 4 q^{27} + 32 q^{28} + 16 q^{30} - 32 q^{31} + 2 q^{33} + 24 q^{36} - 36 q^{37} + 8 q^{40} - 64 q^{42} + 8 q^{45} - 4 q^{48} + 16 q^{51} + 88 q^{52} + 12 q^{55} + 40 q^{57} + 8 q^{58} - 80 q^{60} + 4 q^{63} - 28 q^{67} - 40 q^{70} + 48 q^{72} - 44 q^{75} + 96 q^{76} - 40 q^{78} - 52 q^{81} + 8 q^{82} - 8 q^{85} + 16 q^{87} - 24 q^{88} - 16 q^{90} - 48 q^{91} + 58 q^{93} + 128 q^{96} + 76 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.2.k.a 165.k 15.e $4$ $1.318$ \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
165.2.k.b 165.k 15.e $4$ $1.318$ \(\Q(\zeta_{8})\) None \(4\) \(0\) \(8\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
165.2.k.c 165.k 15.e $16$ $1.318$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(-2\) \(-8\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}-\beta _{15}q^{3}+(-\beta _{1}-\beta _{3}-\beta _{13}+\cdots)q^{4}+\cdots\)
165.2.k.d 165.k 15.e $16$ $1.318$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(4\) \(8\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(\beta _{1}+\beta _{3}+\beta _{13}+\cdots)q^{4}+\cdots\)