Properties

Label 666.2.bf
Level $666$
Weight $2$
Character orbit 666.bf
Rep. character $\chi_{666}(245,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $152$
Newform subspaces $1$
Sturm bound $228$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 333 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(228\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).

Total New Old
Modular forms 472 152 320
Cusp forms 440 152 288
Eisenstein series 32 0 32

Trace form

\( 152 q - 12 q^{5} - 4 q^{9} + 4 q^{12} + 8 q^{13} - 12 q^{15} + 76 q^{16} + 4 q^{19} - 12 q^{20} + 36 q^{23} - 36 q^{27} - 12 q^{28} - 16 q^{31} - 20 q^{37} - 28 q^{39} - 48 q^{41} - 20 q^{42} + 4 q^{43}+ \cdots - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(666, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
666.2.bf.a 666.bf 333.af $152$ $5.318$ None 666.2.ba.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(666, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)