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Properties

Label 164.2.g
Level $164$
Weight $2$
Character orbit 164.g
Rep. character $\chi_{164}(37,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $16$
Newform subspaces $1$
Sturm bound $42$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 164.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 1 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(164, [\chi])\).

Total New Old
Modular forms 96 16 80
Cusp forms 72 16 56
Eisenstein series 24 0 24

Trace form

\( 16 q - 2 q^{3} - 4 q^{5} + 18 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{3} - 4 q^{5} + 18 q^{9} + q^{11} - q^{17} + 9 q^{19} - 15 q^{21} - 18 q^{23} - 22 q^{25} + 10 q^{27} + 4 q^{29} + 3 q^{31} - 15 q^{33} + q^{35} + 4 q^{37} + 4 q^{39} - 36 q^{41} - 4 q^{43} - 24 q^{45} - 19 q^{47} - 16 q^{49} - 51 q^{51} - 19 q^{53} + 42 q^{55} + 16 q^{57} - 32 q^{59} + 6 q^{61} + 50 q^{63} + 16 q^{65} + 47 q^{67} + 38 q^{69} - 3 q^{71} + 42 q^{73} - 15 q^{75} - 33 q^{77} + 18 q^{79} - 8 q^{81} + 52 q^{83} + 58 q^{85} - 34 q^{87} + 16 q^{89} + 84 q^{91} + 88 q^{93} + 16 q^{95} + 34 q^{97} - 98 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(164, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
164.2.g.a 164.g 41.d $16$ $1.310$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{2}q^{3}+(\beta _{3}+\beta _{4}-\beta _{6}+\beta _{7}-\beta _{9}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(164, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(164, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 2}\)