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Properties

Label 882.2.l
Level $882$
Weight $2$
Character orbit 882.l
Rep. character $\chi_{882}(227,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $3$
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.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(336\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 368 80 288
Cusp forms 304 80 224
Eisenstein series 64 0 64

Trace form

\( 80 q - 80 q^{4} + 4 q^{9} + O(q^{10}) \) \( 80 q - 80 q^{4} + 4 q^{9} - 24 q^{11} - 6 q^{13} + 30 q^{15} + 80 q^{16} + 18 q^{17} + 16 q^{18} - 6 q^{23} - 40 q^{25} - 12 q^{26} - 36 q^{27} - 6 q^{29} - 4 q^{30} - 4 q^{36} + 2 q^{37} + 20 q^{39} + 6 q^{41} + 2 q^{43} + 24 q^{44} + 30 q^{45} - 6 q^{46} + 36 q^{47} - 18 q^{51} + 6 q^{52} + 60 q^{53} - 18 q^{54} - 26 q^{57} - 6 q^{58} - 60 q^{59} - 30 q^{60} - 36 q^{62} - 80 q^{64} - 24 q^{66} + 28 q^{67} - 18 q^{68} + 42 q^{69} - 16 q^{72} - 18 q^{74} - 60 q^{75} + 8 q^{78} - 56 q^{79} + 60 q^{81} + 24 q^{85} - 48 q^{86} + 24 q^{87} + 24 q^{89} - 18 q^{90} + 6 q^{92} + 42 q^{93} - 6 q^{97} + 50 q^{99} + O(q^{100}) \)

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.l.a 882.l 63.i $16$ $7.043$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{4}q^{2}+\beta _{6}q^{3}-q^{4}+(-\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
882.2.l.b 882.l 63.i $16$ $7.043$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}-\beta _{8}q^{3}-q^{4}+(\beta _{5}+\beta _{7}-\beta _{9}+\cdots)q^{5}+\cdots\)
882.2.l.c 882.l 63.i $48$ $7.043$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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