Properties

Label 42.3.g
Level $42$
Weight $3$
Character orbit 42.g
Rep. character $\chi_{42}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 42.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(42, [\chi])\).

Total New Old
Modular forms 40 4 36
Cusp forms 24 4 20
Eisenstein series 16 0 16

Trace form

\( 4 q + 6 q^{3} - 4 q^{4} + 12 q^{5} - 10 q^{7} + 6 q^{9} - 24 q^{10} - 12 q^{11} - 12 q^{12} + 24 q^{14} + 24 q^{15} - 8 q^{16} - 48 q^{17} - 42 q^{19} + 24 q^{23} + 22 q^{25} + 96 q^{26} + 40 q^{28} - 24 q^{30}+ \cdots - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(42, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
42.3.g.a 42.g 7.d $4$ $1.144$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 42.3.g.a \(0\) \(6\) \(12\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(2+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(42, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(42, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)