Properties

Label 84.2.b
Level $84$
Weight $2$
Character orbit 84.b
Rep. character $\chi_{84}(55,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $32$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 84.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(19\)

Dimensions

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

Total New Old
Modular forms 20 8 12
Cusp forms 12 8 4
Eisenstein series 8 0 8

Trace form

\( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 8 q^{9} - 2 q^{14} - 14 q^{16} - 2 q^{18} - 4 q^{21} + 12 q^{22} - 16 q^{25} + 18 q^{28} - 16 q^{29} + 16 q^{30} + 18 q^{32} + 2 q^{36} - 24 q^{37} - 16 q^{42} + 28 q^{44}+ \cdots + 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
84.2.b.a 84.b 28.d $4$ $0.671$ \(\Q(\sqrt{-14 +2 \sqrt{17}})\) None 84.2.b.a \(-1\) \(-4\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
84.2.b.b 84.b 28.d $4$ $0.671$ \(\Q(\sqrt{-14 +2 \sqrt{17}})\) None 84.2.b.a \(-1\) \(4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(84, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)