Properties

Label 168.3.d
Level $168$
Weight $3$
Character orbit 168.d
Rep. character $\chi_{168}(113,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 168.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(168, [\chi])\).

Total New Old
Modular forms 72 12 60
Cusp forms 56 12 44
Eisenstein series 16 0 16

Trace form

\( 12 q - 4 q^{3} + 12 q^{9} - 32 q^{13} - 56 q^{15} + 24 q^{19} - 12 q^{25} + 116 q^{27} + 16 q^{31} - 16 q^{37} - 8 q^{39} - 112 q^{43} - 72 q^{45} + 84 q^{49} + 40 q^{51} + 16 q^{55} + 96 q^{57} + 208 q^{61}+ \cdots - 192 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(168, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
168.3.d.a 168.d 3.b $12$ $4.578$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 168.3.d.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(-\beta _{3}-\beta _{11})q^{5}+\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(168, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(168, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)