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Properties

Label 2646.2.e
Level $2646$
Weight $2$
Character orbit 2646.e
Rep. character $\chi_{2646}(1549,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $20$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 20 \)
Sturm bound: \(1008\)
Trace bound: \(13\)
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 80 1024
Cusp forms 912 80 832
Eisenstein series 192 0 192

Trace form

\( 80 q + 80 q^{4} - 4 q^{5} + O(q^{10}) \) \( 80 q + 80 q^{4} - 4 q^{5} + 8 q^{11} - 2 q^{13} + 80 q^{16} - 14 q^{17} + 4 q^{19} - 4 q^{20} + 2 q^{23} - 40 q^{25} - 16 q^{26} - 18 q^{29} + 4 q^{31} - 2 q^{37} - 12 q^{38} - 6 q^{41} - 2 q^{43} + 8 q^{44} + 6 q^{46} + 12 q^{47} - 2 q^{52} + 32 q^{53} + 12 q^{55} - 6 q^{58} + 44 q^{59} + 16 q^{61} + 44 q^{62} + 80 q^{64} - 4 q^{65} + 28 q^{67} - 14 q^{68} + 76 q^{71} + 28 q^{73} - 6 q^{74} + 4 q^{76} + 64 q^{79} - 4 q^{80} + 16 q^{83} - 24 q^{85} + 20 q^{86} - 36 q^{89} + 2 q^{92} + 24 q^{94} - 84 q^{95} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.e.a 2646.e 63.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-1+\zeta_{6})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
2646.2.e.b 2646.e 63.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}-q^{8}-3\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
2646.2.e.c 2646.e 63.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}-q^{8}-3\zeta_{6}q^{11}+2\zeta_{6}q^{13}+\cdots\)
2646.2.e.d 2646.e 63.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(1-\zeta_{6})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
2646.2.e.e 2646.e 63.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(3-3\zeta_{6})q^{5}-q^{8}+(-3+\cdots)q^{10}+\cdots\)
2646.2.e.f 2646.e 63.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+q^{8}+\cdots\)
2646.2.e.g 2646.e 63.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+q^{8}+\cdots\)
2646.2.e.h 2646.e 63.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(-2+2\zeta_{6})q^{5}+q^{8}+\cdots\)
2646.2.e.i 2646.e 63.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(2-2\zeta_{6})q^{5}+q^{8}+(2+\cdots)q^{10}+\cdots\)
2646.2.e.j 2646.e 63.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+q^{8}+(3+\cdots)q^{10}+\cdots\)
2646.2.e.k 2646.e 63.h $4$ $21.128$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-4\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}-q^{8}+\cdots\)
2646.2.e.l 2646.e 63.h $4$ $21.128$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-4\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{5}-q^{8}+(-\beta _{1}+\cdots)q^{10}+\cdots\)
2646.2.e.m 2646.e 63.h $4$ $21.128$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(4\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+q^{8}+\cdots\)
2646.2.e.n 2646.e 63.h $4$ $21.128$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(4\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+q^{8}+(\beta _{1}+\cdots)q^{10}+\cdots\)
2646.2.e.o 2646.e 63.h $6$ $21.128$ 6.0.309123.1 None \(-6\) \(0\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-2+2\beta _{4}-\beta _{5})q^{5}+\cdots\)
2646.2.e.p 2646.e 63.h $6$ $21.128$ 6.0.309123.1 None \(6\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots\)
2646.2.e.q 2646.e 63.h $8$ $21.128$ \(\Q(\zeta_{24})\) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}-2\zeta_{24}^{7}q^{5}-q^{8}+2\zeta_{24}^{7}q^{10}+\cdots\)
2646.2.e.r 2646.e 63.h $8$ $21.128$ 8.0.3317760000.3 None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+\beta _{7}q^{5}-q^{8}-\beta _{7}q^{10}+\cdots\)
2646.2.e.s 2646.e 63.h $8$ $21.128$ 8.0.\(\cdots\).2 None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}-\beta _{4}q^{5}+q^{8}-\beta _{4}q^{10}+\cdots\)
2646.2.e.t 2646.e 63.h $8$ $21.128$ \(\Q(\zeta_{24})\) None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}-\zeta_{24}^{7}q^{5}+q^{8}-\zeta_{24}^{7}q^{10}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \cong \)