Properties

Label 84.3.d
Level $84$
Weight $3$
Character orbit 84.d
Rep. character $\chi_{84}(13,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 84.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(84, [\chi])\).

Total New Old
Modular forms 38 2 36
Cusp forms 26 2 24
Eisenstein series 12 0 12

Trace form

\( 2 q - 14 q^{7} - 6 q^{9} + O(q^{10}) \) \( 2 q - 14 q^{7} - 6 q^{9} + 36 q^{11} - 24 q^{15} + 36 q^{23} - 46 q^{25} + 36 q^{29} + 20 q^{37} - 72 q^{39} - 76 q^{43} + 98 q^{49} + 48 q^{51} + 36 q^{53} + 72 q^{57} + 42 q^{63} - 288 q^{65} + 52 q^{67} + 36 q^{71} - 252 q^{77} + 4 q^{79} + 18 q^{81} + 192 q^{85} + 144 q^{93} + 288 q^{95} - 108 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(84, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
84.3.d.a 84.d 7.b $2$ $2.289$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}-4\zeta_{6}q^{5}-7q^{7}-3q^{9}+18q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(84, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)