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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
165.2.k.a \(4\) \(1.318\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(-8\) \(-8\) \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
165.2.k.b \(4\) \(1.318\) \(\Q(\zeta_{8})\) None \(4\) \(0\) \(8\) \(-8\) \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
165.2.k.c \(16\) \(1.318\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(-2\) \(-8\) \(8\) \(q+\beta _{3}q^{2}-\beta _{15}q^{3}+(-\beta _{1}-\beta _{3}-\beta _{13}+\cdots)q^{4}+\cdots\)
165.2.k.d \(16\) \(1.318\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(4\) \(8\) \(8\) \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(\beta _{1}+\beta _{3}+\beta _{13}+\cdots)q^{4}+\cdots\)