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Properties

Label 666.2.ba
Level $666$
Weight $2$
Character orbit 666.ba
Rep. character $\chi_{666}(23,\cdot)$
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.ba (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

\( 152 q + 8 q^{9} + O(q^{10}) \) \( 152 q + 8 q^{9} - 8 q^{12} - 4 q^{13} - 152 q^{16} + 4 q^{19} - 36 q^{21} + 36 q^{23} + 36 q^{27} - 12 q^{28} + 36 q^{29} - 4 q^{31} - 20 q^{37} + 20 q^{39} - 96 q^{41} - 56 q^{42} - 8 q^{43} + 24 q^{47} - 80 q^{49} + 8 q^{51} + 4 q^{52} + 12 q^{55} - 20 q^{57} - 28 q^{61} - 36 q^{62} - 36 q^{63} + 32 q^{66} + 52 q^{69} + 48 q^{71} - 36 q^{74} + 100 q^{75} - 4 q^{76} - 48 q^{78} - 8 q^{79} - 56 q^{81} + 24 q^{82} + 40 q^{87} + 36 q^{89} + 60 q^{90} + 60 q^{91} - 36 q^{92} + 72 q^{93} - 48 q^{95} + 44 q^{97} - 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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

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

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