Properties

Label 165.2.c
Level $165$
Weight $2$
Character orbit 165.c
Rep. character $\chi_{165}(34,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $48$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(4\)
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 12 16
Cusp forms 20 12 8
Eisenstein series 8 0 8

Trace form

\( 12 q - 12 q^{4} + 4 q^{5} - 4 q^{6} - 12 q^{9} + O(q^{10}) \) \( 12 q - 12 q^{4} + 4 q^{5} - 4 q^{6} - 12 q^{9} + 12 q^{10} - 16 q^{14} + 4 q^{16} + 16 q^{19} + 4 q^{20} - 8 q^{21} + 12 q^{24} - 4 q^{25} - 24 q^{26} + 16 q^{30} - 16 q^{34} + 12 q^{36} + 8 q^{39} - 28 q^{40} + 8 q^{44} - 4 q^{45} + 32 q^{46} - 12 q^{49} + 8 q^{50} - 8 q^{51} + 4 q^{54} + 96 q^{56} - 8 q^{60} - 40 q^{61} - 44 q^{64} + 40 q^{65} + 8 q^{66} - 16 q^{70} - 48 q^{71} + 32 q^{74} - 64 q^{76} + 32 q^{79} - 52 q^{80} + 12 q^{81} + 40 q^{85} - 16 q^{86} - 40 q^{89} - 12 q^{90} + 48 q^{94} - 48 q^{95} - 28 q^{96} + O(q^{100}) \)

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.c.a 165.c 5.b $6$ $1.318$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
165.2.c.b 165.c 5.b $6$ $1.318$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)