Properties

Label 84.2.f
Level $84$
Weight $2$
Character orbit 84.f
Rep. character $\chi_{84}(41,\cdot)$
Character field $\Q$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
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 22 2 20
Cusp forms 10 2 8
Eisenstein series 12 0 12

Trace form

\( 2 q + 4 q^{7} - 6 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{7} - 6 q^{9} - 6 q^{21} - 10 q^{25} + 20 q^{37} + 24 q^{39} - 16 q^{43} + 2 q^{49} + 12 q^{57} - 12 q^{63} - 32 q^{67} - 8 q^{79} + 18 q^{81} + 24 q^{91} - 36 q^{93} + O(q^{100}) \)

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.f.a \(2\) \(0.671\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{6}q^{3}+(2-\zeta_{6})q^{7}-3q^{9}+4\zeta_{6}q^{13}+\cdots\)

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

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