Properties

Label 2646.2.f
Level $2646$
Weight $2$
Character orbit 2646.f
Rep. character $\chi_{2646}(883,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $82$
Newform subspaces $19$
Sturm bound $1008$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 19 \)
Sturm bound: \(1008\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 1104 82 1022
Cusp forms 912 82 830
Eisenstein series 192 0 192

Trace form

\( 82 q + q^{2} - 41 q^{4} - 4 q^{5} - 2 q^{8} + O(q^{10}) \) \( 82 q + q^{2} - 41 q^{4} - 4 q^{5} - 2 q^{8} + 5 q^{11} + 2 q^{13} - 41 q^{16} - 2 q^{17} - 10 q^{19} - 4 q^{20} + 3 q^{22} + 14 q^{23} - 35 q^{25} + 4 q^{26} - 6 q^{29} + 8 q^{31} + q^{32} + 3 q^{34} - 16 q^{37} - 13 q^{38} - 27 q^{41} + 5 q^{43} - 10 q^{44} + 12 q^{46} + 6 q^{47} + 19 q^{50} + 2 q^{52} + 8 q^{53} - 24 q^{55} + 6 q^{58} + 11 q^{59} + 8 q^{61} + 16 q^{62} + 82 q^{64} + 44 q^{65} + 23 q^{67} + q^{68} + 16 q^{71} - 34 q^{73} + 8 q^{74} + 5 q^{76} - 4 q^{79} + 8 q^{80} + 18 q^{82} - 56 q^{83} - 24 q^{85} + 7 q^{86} + 3 q^{88} - 12 q^{89} + 14 q^{92} - 6 q^{94} - 36 q^{95} - q^{97} + O(q^{100}) \)

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.f.a 2646.f 9.c $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
2646.2.f.b 2646.f 9.c $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
2646.2.f.c 2646.f 9.c $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
2646.2.f.d 2646.f 9.c $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
2646.2.f.e 2646.f 9.c $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}-q^{8}+\cdots\)
2646.2.f.f 2646.f 9.c $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-q^{8}+\cdots\)
2646.2.f.g 2646.f 9.c $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{8}+(-3+3\zeta_{6})q^{11}+\cdots\)
2646.2.f.h 2646.f 9.c $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-q^{8}+\cdots\)
2646.2.f.i 2646.f 9.c $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}-q^{8}+\cdots\)
2646.2.f.j 2646.f 9.c $4$ $21.128$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
2646.2.f.k 2646.f 9.c $4$ $21.128$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
2646.2.f.l 2646.f 9.c $6$ $21.128$ 6.0.309123.1 None \(-3\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-1+\beta _{4})q^{4}-\beta _{2}q^{5}+q^{8}+\cdots\)
2646.2.f.m 2646.f 9.c $6$ $21.128$ 6.0.309123.1 None \(-3\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+\beta _{2}q^{5}+q^{8}+\cdots\)
2646.2.f.n 2646.f 9.c $6$ $21.128$ 6.0.309123.1 None \(3\) \(0\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+(-2+2\beta _{4}+\cdots)q^{5}+\cdots\)
2646.2.f.o 2646.f 9.c $6$ $21.128$ 6.0.309123.1 None \(3\) \(0\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+(2-2\beta _{4}+\cdots)q^{5}+\cdots\)
2646.2.f.p 2646.f 9.c $8$ $21.128$ 8.0.\(\cdots\).2 None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}-\beta _{4}q^{5}+q^{8}+\cdots\)
2646.2.f.q 2646.f 9.c $8$ $21.128$ \(\Q(\zeta_{24})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{24}q^{2}+(-1+\zeta_{24})q^{4}-\zeta_{24}^{7}q^{5}+\cdots\)
2646.2.f.r 2646.f 9.c $8$ $21.128$ \(\Q(\zeta_{24})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{24}q^{2}+(-1+\zeta_{24})q^{4}-2\zeta_{24}^{7}q^{5}+\cdots\)
2646.2.f.s 2646.f 9.c $8$ $21.128$ 8.0.3317760000.3 None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+(-1+\beta _{3})q^{4}+\beta _{7}q^{5}-q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)