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Properties

Label 165.4.f
Level $165$
Weight $4$
Character orbit 165.f
Rep. character $\chi_{165}(131,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 165.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(165, [\chi])\).

Total New Old
Modular forms 76 48 28
Cusp forms 68 48 20
Eisenstein series 8 0 8

Trace form

\( 48 q - 4 q^{3} + 192 q^{4} - 28 q^{9} + O(q^{10}) \) \( 48 q - 4 q^{3} + 192 q^{4} - 28 q^{9} - 48 q^{12} - 40 q^{15} + 1248 q^{16} + 372 q^{22} - 1200 q^{25} - 628 q^{27} - 24 q^{31} - 608 q^{33} - 1464 q^{34} + 444 q^{36} - 264 q^{37} + 2392 q^{42} + 584 q^{48} - 1848 q^{49} + 60 q^{55} - 5040 q^{58} - 1620 q^{60} + 7920 q^{64} - 4236 q^{66} - 168 q^{67} + 3872 q^{69} - 1080 q^{70} + 100 q^{75} + 1048 q^{78} + 8164 q^{81} + 9720 q^{82} - 948 q^{88} - 2256 q^{91} - 3584 q^{93} - 864 q^{97} - 3184 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.4.f.a 165.f 33.d $48$ $9.735$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(165, [\chi]) \cong \)