Properties

Label 666.2.bs
Level $666$
Weight $2$
Character orbit 666.bs
Rep. character $\chi_{666}(17,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $168$
Newform subspaces $2$
Sturm bound $228$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.bs (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 2 \)
Sturm bound: \(228\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 1464 168 1296
Cusp forms 1272 168 1104
Eisenstein series 192 0 192

Trace form

\( 168 q + O(q^{10}) \) \( 168 q + 48 q^{31} + 144 q^{34} + 96 q^{37} + 24 q^{40} + 96 q^{43} + 96 q^{46} - 48 q^{49} + 12 q^{58} + 96 q^{67} - 48 q^{70} + 48 q^{79} + 48 q^{82} - 48 q^{88} + 48 q^{91} - 144 q^{94} - 240 q^{97} + O(q^{100}) \)

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.bs.a 666.bs 111.q $72$ $5.318$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$
666.2.bs.b 666.bs 111.q $96$ $5.318$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$

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

\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)