Properties

Label 666.2.be
Level $666$
Weight $2$
Character orbit 666.be
Rep. character $\chi_{666}(125,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $40$
Newform subspaces $4$
Sturm bound $228$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(228\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 488 40 448
Cusp forms 424 40 384
Eisenstein series 64 0 64

Trace form

\( 40 q + O(q^{10}) \) \( 40 q + 12 q^{13} + 20 q^{16} - 24 q^{19} + 16 q^{22} + 24 q^{28} + 8 q^{31} + 64 q^{37} + 12 q^{40} + 8 q^{43} + 16 q^{46} + 36 q^{49} - 12 q^{52} - 16 q^{55} - 12 q^{58} + 12 q^{61} - 96 q^{67} + 16 q^{70} + 24 q^{76} - 88 q^{79} - 20 q^{82} + 32 q^{88} - 88 q^{91} + 16 q^{94} + 4 q^{97} + O(q^{100}) \)

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.be.a 666.be 111.m $8$ $5.318$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{5}+\cdots\)
666.2.be.b 666.be 111.m $8$ $5.318$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(2\zeta_{24}^{3}+2\zeta_{24}^{7})q^{5}+\cdots\)
666.2.be.c 666.be 111.m $8$ $5.318$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{5}+\cdots\)
666.2.be.d 666.be 111.m $16$ $5.318$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{10}q^{2}-\beta _{9}q^{4}+(\beta _{1}+\beta _{7})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)

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

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