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Properties

Label 891.2.e
Level $891$
Weight $2$
Character orbit 891.e
Rep. character $\chi_{891}(298,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $22$
Sturm bound $216$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 22 \)
Sturm bound: \(216\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(891, [\chi])\).

Total New Old
Modular forms 240 80 160
Cusp forms 192 80 112
Eisenstein series 48 0 48

Trace form

\( 80 q - 40 q^{4} + 10 q^{7} + O(q^{10}) \) \( 80 q - 40 q^{4} + 10 q^{7} + 10 q^{13} - 40 q^{16} - 20 q^{19} - 46 q^{25} - 80 q^{28} + 34 q^{31} + 60 q^{34} - 8 q^{37} + 60 q^{40} + 40 q^{43} - 72 q^{46} - 54 q^{49} + 4 q^{52} + 12 q^{55} - 36 q^{58} - 26 q^{61} + 32 q^{64} - 8 q^{67} - 24 q^{70} + 4 q^{73} + 100 q^{76} + 10 q^{79} + 48 q^{82} + 12 q^{85} - 76 q^{91} - 60 q^{94} + 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(891, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
891.2.e.a 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
891.2.e.b 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
891.2.e.c 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots\)
891.2.e.d 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.e 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.f 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.g 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
891.2.e.h 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots\)
891.2.e.i 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
891.2.e.j 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.k 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.l 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.m 891.e 9.c $4$ $7.115$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots\)
891.2.e.n 891.e 9.c $4$ $7.115$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(-1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
891.2.e.o 891.e 9.c $4$ $7.115$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(1\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
891.2.e.p 891.e 9.c $4$ $7.115$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
891.2.e.q 891.e 9.c $6$ $7.115$ 6.0.954288.1 None \(-1\) \(0\) \(2\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
891.2.e.r 891.e 9.c $6$ $7.115$ 6.0.2101707.2 None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots\)
891.2.e.s 891.e 9.c $6$ $7.115$ 6.0.2101707.2 None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots\)
891.2.e.t 891.e 9.c $6$ $7.115$ 6.0.954288.1 None \(1\) \(0\) \(-2\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
891.2.e.u 891.e 9.c $8$ $7.115$ 8.0.22581504.2 None \(-2\) \(0\) \(-8\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
891.2.e.v 891.e 9.c $8$ $7.115$ 8.0.22581504.2 None \(2\) \(0\) \(8\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(891, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(891, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)