Properties

Label 165.2.f
Level $165$
Weight $2$
Character orbit 165.f
Rep. character $\chi_{165}(131,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $48$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 28 16 12
Cusp forms 20 16 4
Eisenstein series 8 0 8

Trace form

\( 16q - 4q^{3} + 16q^{4} + 8q^{9} + O(q^{10}) \) \( 16q - 4q^{3} + 16q^{4} + 8q^{9} - 12q^{12} - 4q^{15} - 16q^{16} - 8q^{22} - 16q^{25} + 20q^{27} + 4q^{33} - 32q^{34} - 24q^{36} + 16q^{37} - 8q^{42} - 52q^{48} - 16q^{49} + 8q^{55} + 8q^{58} + 12q^{60} + 24q^{66} + 88q^{67} - 40q^{69} + 24q^{70} + 4q^{75} + 88q^{78} + 16q^{81} - 56q^{82} + 16q^{88} + 16q^{91} - 56q^{93} - 48q^{97} + 56q^{99} + O(q^{100}) \)

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.f.a \(8\) \(1.318\) 8.0.619810816.2 None \(0\) \(-2\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots\)
165.2.f.b \(8\) \(1.318\) 8.0.619810816.2 None \(0\) \(-2\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)