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Properties

Label 84.6.k
Level $84$
Weight $6$
Character orbit 84.k
Rep. character $\chi_{84}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $26$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 84.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(84, [\chi])\).

Total New Old
Modular forms 172 26 146
Cusp forms 148 26 122
Eisenstein series 24 0 24

Trace form

\( 26 q + 103 q^{7} + 300 q^{9} + O(q^{10}) \) \( 26 q + 103 q^{7} + 300 q^{9} - 474 q^{15} - 3753 q^{19} - 4167 q^{21} - 8833 q^{25} + 9411 q^{31} + 1053 q^{33} + 5915 q^{37} - 1827 q^{39} + 4010 q^{43} + 14733 q^{45} - 23311 q^{49} - 25575 q^{51} + 26820 q^{57} + 61230 q^{61} - 39720 q^{63} - 19751 q^{67} + 119169 q^{73} + 102987 q^{75} - 60323 q^{79} - 1332 q^{81} + 145932 q^{85} - 11088 q^{87} - 42081 q^{91} + 83448 q^{93} - 407142 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(84, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
84.6.k.a 84.k 21.g $2$ $13.472$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 84.6.k.a \(0\) \(-27\) \(0\) \(25\) $\mathrm{U}(1)[D_{6}]$ \(q+(-9-9\zeta_{6})q^{3}+(-62+149\zeta_{6})q^{7}+\cdots\)
84.6.k.b 84.k 21.g $24$ $13.472$ None 84.6.k.b \(0\) \(27\) \(0\) \(78\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{6}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(84, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)