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Properties

Label 164.3.h
Level $164$
Weight $3$
Character orbit 164.h
Rep. character $\chi_{164}(85,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $28$
Newform subspaces $1$
Sturm bound $63$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 164.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(63\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(164, [\chi])\).

Total New Old
Modular forms 180 28 152
Cusp forms 156 28 128
Eisenstein series 24 0 24

Trace form

\( 28 q - 8 q^{3} + 24 q^{9} + O(q^{10}) \) \( 28 q - 8 q^{3} + 24 q^{9} + 36 q^{13} + 12 q^{15} - 56 q^{17} - 48 q^{19} + 52 q^{21} + 52 q^{27} - 52 q^{29} + 116 q^{33} + 16 q^{35} + 112 q^{37} + 16 q^{39} - 16 q^{41} - 140 q^{43} + 16 q^{47} - 216 q^{49} - 80 q^{51} - 140 q^{53} - 88 q^{55} + 56 q^{57} + 144 q^{61} - 88 q^{63} - 268 q^{65} - 136 q^{67} + 20 q^{69} - 216 q^{71} - 228 q^{73} - 212 q^{75} + 372 q^{77} - 300 q^{79} + 680 q^{83} - 248 q^{85} - 100 q^{87} - 188 q^{89} + 284 q^{91} + 448 q^{93} + 204 q^{95} + 636 q^{97} + 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(164, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
164.3.h.a 164.h 41.e $28$ $4.469$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{3}^{\mathrm{old}}(164, [\chi])\) into lower level spaces

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