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Properties

Label 164.2.o
Level $164$
Weight $2$
Character orbit 164.o
Rep. character $\chi_{164}(7,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $304$
Newform subspaces $2$
Sturm bound $42$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 164.o (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q(\zeta_{40})\)
Newform subspaces: \( 2 \)
Sturm bound: \(42\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 368 368 0
Cusp forms 304 304 0
Eisenstein series 64 64 0

Trace form

\( 304 q - 16 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 16 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 32 q^{13} - 4 q^{14} - 12 q^{16} - 4 q^{17} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25}+ \cdots + 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
164.2.o.a 164.o 164.o $16$ $1.310$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-1}) \) 164.2.o.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{40}]$ \(q+(\zeta_{40}^{2}-\zeta_{40}^{6}+\zeta_{40}^{8}+\zeta_{40}^{10}+\cdots)q^{2}+\cdots\)
164.2.o.b 164.o 164.o $288$ $1.310$ None 164.2.o.b \(-12\) \(0\) \(-32\) \(0\) $\mathrm{SU}(2)[C_{40}]$