Properties

Label 2646.2.t
Level $2646$
Weight $2$
Character orbit 2646.t
Rep. character $\chi_{2646}(1979,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $3$
Sturm bound $1008$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(1008\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2646, [\chi])\).

Total New Old
Modular forms 1104 80 1024
Cusp forms 912 80 832
Eisenstein series 192 0 192

Trace form

\( 80 q + 40 q^{4} + O(q^{10}) \) \( 80 q + 40 q^{4} + 6 q^{13} - 40 q^{16} + 18 q^{17} + 80 q^{25} - 12 q^{26} + 6 q^{29} - 6 q^{31} + 2 q^{37} + 6 q^{41} + 2 q^{43} + 24 q^{44} - 6 q^{46} - 18 q^{47} + 60 q^{53} + 12 q^{58} + 30 q^{59} + 60 q^{61} - 36 q^{62} - 80 q^{64} + 42 q^{65} - 14 q^{67} + 36 q^{68} + 28 q^{79} + 24 q^{85} + 24 q^{89} - 6 q^{92} - 114 q^{95} + 6 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2646, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2646.2.t.a 2646.t 63.s $16$ $21.128$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{5}+\beta _{7})q^{2}+(1-\beta _{8})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
2646.2.t.b 2646.t 63.s $16$ $21.128$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(1-\beta _{8})q^{4}+(\beta _{12}+\beta _{14}+\cdots)q^{5}+\cdots\)
2646.2.t.c 2646.t 63.s $48$ $21.128$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2646, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)