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Properties

Label 164.2.k
Level $164$
Weight $2$
Character orbit 164.k
Rep. character $\chi_{164}(25,\cdot)$
Character field $\Q(\zeta_{10})$
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.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{10})\)
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

\( 16 q + 4 q^{5} - 30 q^{9} + O(q^{10}) \) \( 16 q + 4 q^{5} - 30 q^{9} - 5 q^{11} - 10 q^{15} + 5 q^{17} + 15 q^{19} + 19 q^{21} + 12 q^{23} - 2 q^{25} + 20 q^{29} + 3 q^{31} - 25 q^{33} + 5 q^{35} + 2 q^{37} - 28 q^{39} - 4 q^{41} - 22 q^{43} - 48 q^{45} + 15 q^{47} - 28 q^{49} + 17 q^{51} + 25 q^{53} - 8 q^{57} + 8 q^{59} - 46 q^{61} - 40 q^{63} - 10 q^{65} - 45 q^{67} + 10 q^{69} + 15 q^{71} + 34 q^{73} + 135 q^{75} + 23 q^{77} + 108 q^{81} + 12 q^{83} + 14 q^{87} + 60 q^{93} - 30 q^{95} - 40 q^{97} + 70 q^{99} + O(q^{100}) \)

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.k.a 164.k 41.f $16$ $1.310$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{1}q^{3}-\beta _{12}q^{5}+(-\beta _{9}+\beta _{14})q^{7}+\cdots\)

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

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