Properties

Label 84.2.i
Level $84$
Weight $2$
Character orbit 84.i
Rep. character $\chi_{84}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $2$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 84.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(84, [\chi])\).

Total New Old
Modular forms 44 2 42
Cusp forms 20 2 18
Eisenstein series 24 0 24

Trace form

\( 2q + q^{3} + 2q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} + 2q^{5} + q^{7} - q^{9} - 2q^{11} - 6q^{13} + 4q^{15} - 8q^{17} + q^{19} - 4q^{21} - 8q^{23} + q^{25} - 2q^{27} + 8q^{29} - 3q^{31} + 2q^{33} + 10q^{35} + q^{37} - 3q^{39} + 12q^{41} + 22q^{43} + 2q^{45} - 6q^{47} - 13q^{49} + 8q^{51} + 12q^{53} - 8q^{55} + 2q^{57} - 4q^{59} + 6q^{61} - 5q^{63} - 6q^{65} - 13q^{67} - 16q^{69} - 20q^{71} + 11q^{73} - q^{75} + 8q^{77} + 3q^{79} - q^{81} + 4q^{83} - 32q^{85} + 4q^{87} - 3q^{91} + 3q^{93} - 2q^{95} + 20q^{97} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(84, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
84.2.i.a \(2\) \(0.671\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(1\) \(q+\zeta_{6}q^{3}+(2-2\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

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