Properties

Label 84.9.p
Level $84$
Weight $9$
Character orbit 84.p
Rep. character $\chi_{84}(53,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $42$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 84.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(84, [\chi])\).

Total New Old
Modular forms 268 42 226
Cusp forms 244 42 202
Eisenstein series 24 0 24

Trace form

\( 42 q - 4307 q^{7} - 1790 q^{9} + O(q^{10}) \) \( 42 q - 4307 q^{7} - 1790 q^{9} + 57430 q^{13} + 68482 q^{15} + 153723 q^{19} + 154411 q^{21} + 1376167 q^{25} - 2389050 q^{27} - 551843 q^{31} + 1874885 q^{33} + 1614999 q^{37} + 6645319 q^{39} - 6682842 q^{43} - 527785 q^{45} - 5924535 q^{49} - 1103461 q^{51} + 71577224 q^{55} + 8395440 q^{57} + 2064556 q^{61} + 23513124 q^{63} + 5537483 q^{67} - 5588722 q^{69} + 2048483 q^{73} - 49612355 q^{75} - 64909811 q^{79} - 67596854 q^{81} + 139250060 q^{85} - 16321046 q^{87} + 103876909 q^{91} - 21483884 q^{93} - 353400880 q^{97} - 94510994 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(84, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
84.9.p.a $2$ $34.220$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-81\) \(0\) \(-4273\) \(q-3^{4}\zeta_{6}q^{3}+(-2769+1265\zeta_{6})q^{7}+\cdots\)
84.9.p.b $40$ $34.220$ None \(0\) \(81\) \(0\) \(-34\)

Decomposition of \(S_{9}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(84, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)