Properties

Label 165.2.d
Level $165$
Weight $2$
Character orbit 165.d
Rep. character $\chi_{165}(164,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $3$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(23\)

Dimensions

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

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20q - 24q^{4} - 10q^{9} + O(q^{10}) \) \( 20q - 24q^{4} - 10q^{9} - 3q^{15} + 14q^{25} - 20q^{31} + 16q^{34} + 28q^{36} + 37q^{45} - 12q^{49} + 6q^{55} - 54q^{60} + 64q^{64} - 48q^{66} - 30q^{69} + 16q^{70} + 33q^{75} - 34q^{81} - 128q^{91} + 70q^{99} + O(q^{100}) \)

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.d.a \(2\) \(1.318\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(3\) \(0\) \(q-\beta q^{3}+2q^{4}+(1+\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
165.2.d.b \(2\) \(1.318\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(-3\) \(0\) \(q+\beta q^{3}+2q^{4}+(-2+\beta )q^{5}+(-3+\cdots)q^{9}+\cdots\)
165.2.d.c \(16\) \(1.318\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)