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Properties

Label 164.2.m
Level $164$
Weight $2$
Character orbit 164.m
Rep. character $\chi_{164}(5,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $24$
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.m (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{20})\)
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 192 24 168
Cusp forms 144 24 120
Eisenstein series 48 0 48

Trace form

\( 24 q - 2 q^{3} + O(q^{10}) \) \( 24 q - 2 q^{3} + 4 q^{11} + 2 q^{13} + 22 q^{15} + 2 q^{17} - 32 q^{19} + 6 q^{23} - 6 q^{25} - 2 q^{27} - 10 q^{29} - 18 q^{31} + 20 q^{33} - 38 q^{35} - 34 q^{37} - 40 q^{39} + 14 q^{41} + 10 q^{43} - 20 q^{45} - 24 q^{47} - 20 q^{49} - 2 q^{51} + 4 q^{53} - 34 q^{55} - 16 q^{57} + 24 q^{59} + 40 q^{61} - 18 q^{63} - 20 q^{65} + 14 q^{67} + 52 q^{69} + 44 q^{71} + 20 q^{75} + 70 q^{77} + 82 q^{79} + 12 q^{81} - 56 q^{83} + 36 q^{85} + 80 q^{87} + 46 q^{89} - 12 q^{93} + 106 q^{95} + 76 q^{97} + 32 q^{99} + O(q^{100}) \)

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.m.a 164.m 41.g $24$ $1.310$ None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

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

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