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Properties

Label 882.2.f
Level $882$
Weight $2$
Character orbit 882.f
Rep. character $\chi_{882}(295,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $82$
Newform subspaces $19$
Sturm bound $336$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 19 \)
Sturm bound: \(336\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(882, [\chi])\).

Total New Old
Modular forms 368 82 286
Cusp forms 304 82 222
Eisenstein series 64 0 64

Trace form

\( 82 q - q^{2} - 3 q^{3} - 41 q^{4} + 4 q^{5} - 5 q^{6} + 2 q^{8} - 9 q^{9} + O(q^{10}) \) \( 82 q - q^{2} - 3 q^{3} - 41 q^{4} + 4 q^{5} - 5 q^{6} + 2 q^{8} - 9 q^{9} - 5 q^{11} + 2 q^{13} + 4 q^{15} - 41 q^{16} + 2 q^{17} + 10 q^{18} - 10 q^{19} + 4 q^{20} + 3 q^{22} - 14 q^{23} + q^{24} - 35 q^{25} - 4 q^{26} + 36 q^{27} + 6 q^{29} - 12 q^{30} + 8 q^{31} - q^{32} - 5 q^{33} + 3 q^{34} + 3 q^{36} - 16 q^{37} + 13 q^{38} - 28 q^{39} + 27 q^{41} + 5 q^{43} + 10 q^{44} + 40 q^{45} + 12 q^{46} - 6 q^{47} + 3 q^{48} - 19 q^{50} + 29 q^{51} + 2 q^{52} - 8 q^{53} - 11 q^{54} - 24 q^{55} - 9 q^{57} + 6 q^{58} - 11 q^{59} - 8 q^{60} + 8 q^{61} - 16 q^{62} + 82 q^{64} - 44 q^{65} - 32 q^{66} + 23 q^{67} - q^{68} - 32 q^{69} - 16 q^{71} - 5 q^{72} - 34 q^{73} - 8 q^{74} - 7 q^{75} + 5 q^{76} - 38 q^{78} - 4 q^{79} - 8 q^{80} + 35 q^{81} + 18 q^{82} + 56 q^{83} - 24 q^{85} - 7 q^{86} - 34 q^{87} + 3 q^{88} + 12 q^{89} + 52 q^{90} - 14 q^{92} + 16 q^{93} - 6 q^{94} + 36 q^{95} + 4 q^{96} - q^{97} - 50 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
882.2.f.a 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.b 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.c 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.d 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.e 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.f 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.g 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.h 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.i 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.j 882.f 9.c $4$ $7.043$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(-4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(-1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
882.2.f.k 882.f 9.c $4$ $7.043$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(1\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
882.2.f.l 882.f 9.c $6$ $7.043$ 6.0.309123.1 None \(-3\) \(-2\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
882.2.f.m 882.f 9.c $6$ $7.043$ 6.0.309123.1 None \(-3\) \(2\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{4})q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
882.2.f.n 882.f 9.c $6$ $7.043$ 6.0.309123.1 None \(3\) \(-4\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{4})q^{2}+(-1+\beta _{5})q^{3}+\beta _{4}q^{4}+\cdots\)
882.2.f.o 882.f 9.c $6$ $7.043$ 6.0.309123.1 None \(3\) \(4\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{4})q^{2}+(1-\beta _{5})q^{3}+\beta _{4}q^{4}+\cdots\)
882.2.f.p 882.f 9.c $8$ $7.043$ 8.0.3317760000.3 None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{5}-\beta _{6})q^{3}+\cdots\)
882.2.f.q 882.f 9.c $8$ $7.043$ \(\Q(\zeta_{24})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{24}q^{2}+(\zeta_{24}^{6}-\zeta_{24}^{7})q^{3}+(-1+\cdots)q^{4}+\cdots\)
882.2.f.r 882.f 9.c $8$ $7.043$ 8.0.\(\cdots\).2 None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{4})q^{2}+(-\beta _{1}-\beta _{5})q^{3}+\beta _{4}q^{4}+\cdots\)
882.2.f.s 882.f 9.c $8$ $7.043$ \(\Q(\zeta_{24})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{24}q^{2}+(\zeta_{24}^{3}-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)